stock market declines and liquidity jf2009 finalviswanat/stock_market... · acharya, yakov amihud,...
TRANSCRIPT
1
Stock Market Declines and Liquidity
ALLAUDEEN HAMEED, WENJIN KANG, and S. VISWANATHAN*
ABSTRACT
Consistent with recent theoretical models where binding capital constraints lead to sudden liquidity dry-ups, we find that negative market returns decrease stock liquidity, especially during times of tightness in the funding market. The asymmetric effect of changes in aggregate asset values on liquidity and commonality in liquidity cannot be fully explained by changes in demand for liquidity or volatility effects. We document inter-industry spill-over effects in liquidity, which are likely to arise from capital constraints in the market making sector. We also find economically significant returns to supplying liquidity following periods of large drop in market valuations.
*Allaudeen Hameed and Wenjin Kang are from the Department of Finance, NUS Business School, National University of Singapore. S. Viswanathan is from the Fuqua School of Business, Duke University. We thank Viral Acharya, Yakov Amihud, Michael Brandt, Markus Brunnermeier, Andrew Ellul, Bob Engle, Doug Foster, Joel Hasbrouck, David Hsieh, Frank de Jong, Pete Kyle, Ravi Jagannathan, Christine Parlour, David Robinson, Ioanid Rosu, Avanidhar Subrahmanyam, Sheridan Titman, two anonymous referees, and participants at the NBER 2005 microstructure conference, 2007 American Finance Association meeting, 2007 European Finance Association Meeting, 2008 First Erasmus Liquidity Conference, Australian National University, Case Western Reserve University, Erasmus University, Hong Kong University, Hong Kong University of Science and Technology, Nanyang Technological University, National University of Singapore, New York University, Peking University, University of Alberta, University of Evry (France), University of Melbourne, and University of Texas (Austin) for their comments. Hameed and Kang acknowledge financial support from the NUS Academic Research Grants and Viswanathan thanks IIMA Bangalore for their hospitality during year 2005 when this paper was started.
2
In recent theoretical research, the idea that market declines cause asset illiquidity has
received much attention. Liquidity dry-ups are argued to occur because market
participants engage in panic selling (a demand effect), or financial intermediaries
withdraw from providing liquidity (a supply effect), or both. In this paper, we explore
empirically what happens to market liquidity after large market declines and whether
supply effects exist in equity markets. It is difficult to establish the actual identity of
financial intermediaries in equity markets as they could be specialists, floor traders, limit
order providers, or other traders like hedge funds. Furthermore, the actual positions and
balance sheets of these intermediaries are unknown. We therefore take an encompassing
approach by investigating the impact of market declines on various dimensions of
liquidity, including: (a) time-series as well as cross-sectional variation in liquidity; (b)
commonality in liquidity; and (c) cost of liquidity provision.
Theoretical models obtain illiquidity after market declines in a variety of ways. In
collateral-based models, market makers make markets by absorbing temporary liquidity
shocks. However, they also face funding constraints and obtain financing by posting
margins and pledging the securities they hold as collateral. Thus, when stock prices
decline considerably, the intermediaries hit their margin constraints and are forced to
liquidate. In Brunnermeier and Pedersen (2009), for instance, a large market shock
triggers the switch to a low liquidity, high margin equilibrium, where markets are illiquid,
resulting in larger margin requirements. This illiquidity spiral further restricts dealers
from providing market liquidity. Anshuman and Viswanathan (2005) present a slightly
different model where leveraged investors are asked to provide collateral when asset
values fall and decide to endogenously default, leading to asset liquidation. At the same
3
time, market makers face funding constraints as they are able to finance less in the repo
market for the assets they own. Garleanu and Pedersen (2007) show that tighter risk
management by institutions in response to higher volatility in market downturns reduces
their risk bearing capacity and lowers market liquidity. Garleanu and Pedersen also stress
a feedback effect, where the decrease in market liquidity further tightens risk
management. Gromb and Vayanos (2002) emphasize that the reduction in supply of
liquidity due to capital constraints has important welfare and regulatory implications.
Partly motivated by the Long Term Capital Management (LTCM) crisis, the balance
sheets of intermediaries matter in these collateral-based models as the intermediaries face
financial constraints that are often binding precisely when it is most incumbent for them
to provide liquidity.1
In limits-to-arbitrage based models such as Kyle and Xiong (2001) and Xiong
(2001), shocks to noise traders make prices move away from fundamentals and
arbitrageurs provide liquidity and take advantage of the arbitrage opportunities. These
liquidity providers have decreasing absolute risk aversion preferences, or face capital
constraints with mark-to-market losses, and their demand for risky assets declines
following market downturns -- they become liquidity demanders as they liquidate their
positions in risky assets. Mitchell, Pedersen, and Pulvino (2007) show that convertible
hedge funds, which provide liquidity in normal times, were forced to liquidate their
convertible bond positions due to binding capital constraints following large capital
redemptions from investors in 2005 and the large drop in security values during the
LTCM crisis.
4
In the coordination failure models of Bernardo and Welch (2003) and Morris and
Shin (2004), traders face differing trading limits that cause them to sell. Since one trader
hitting his limit may push down the price and make other traders’ limits be hit, early
liquidation gives a better price than late liquidation. Here, traders rush to liquidate
following negative shocks, and when prices fall enough, liquidity black holes emerge,
analogous to a model of bank runs. Vayanos (2004) presents an asset pricing model
where investors have to liquidate when asset prices fall below a lower bound, leading to
liquidation risk being priced. Vayanos links the risk of needing to liquidate to volatility,
especially for stocks with large exposure to market volatility.
While the exact details of the theoretical models above differ, they all predict that
large market declines increase the demand for liquidity as agents liquidate their positions
across many assets and reduce the supply of liquidity as liquidity providers hit their
wealth or funding constraints.
Using the proportional bid-ask spread (as a proportion of the stock’s price) as one
of our key measures of liquidity, we find that changes in spreads are negatively related to
market returns. In particular, large negative market returns have a stronger impact on
weekly changes in a firm’s bid-ask spread than positive returns, and the average spread
increases by 2.8 (6.2) basis points after a (large) market decline. These changes in
liquidity last for about two weeks and then reverse in the subsequent weeks. Moreover,
we find that the impact of negative market returns on liquidity is stronger when financial
intermediaries are more likely to face funding constraints. For example, negative market
returns reduce liquidity more when there are also large declines in the aggregate balance
sheets of financial intermediaries or in the market value of the investment banking
5
sector.2 This asymmetric relation between market returns and liquidity is robust to the
inclusion of firm-level control variables such as lagged own stock returns, turnover, and
buy-sell order imbalance, as well as changes in volatilities as suggested in Vayanos
(2004). Brunnermeier and Pedersen (2009) suggest that a deterioration of dealer capital
leads to greater cross-sectional differences in liquidity of high and low volatility stocks.
Consistent with this flight to liquidity prediction, we find that the impact of market
declines on liquidity is strongest for high volatility firms. Our findings lend support to the
hypothesis that the relation between liquidity and market declines is related to changes in
the supply of liquidity.
Brunnermeier and Pedersen (2009) also suggest that a huge market wide decline
in prices reduces the aggregate collateral of the market making sector, which feeds back
as higher comovement in market liquidity. While there is some research on comovements
in market liquidity in stock and bond markets (Chordia, Roll, Subrahmanyam (2000),
Hasbrouck and Seppi (2001), Huberman and Halka (2001), and others) and evidence that
market making collapsed after the stock market crisis in 1987 (see the Brady commission
report on the 1987 crisis), there is little empirical evidence on the effect of stock market
movements on commonality in liquidity. Naik and Yadav (2003) and Coughenour and
Saad (2004) consider the effect of capital constraints on liquidity commonality. Kamara,
Lou, and Sadka (2008) suggest that the time variation in systematic liquidity is related to
concentration of institutional ownership and index trading. 3 However, the extant
empirical literature does not consider whether liquidity comovement increases
dramatically after large market declines in a manner similar to the finding that stock
return comovement goes up after large market drops (see Ang, Chen, and Xing (2006) on
6
downside risk and especially Ang and Chen (2002) for work on asymmetric correlations
between portfolios).
We document that the commonality in liquidity (spreads) increases during periods
of market declines. Specifically, we find that the liquidity beta increases by 0.31 (0.39)
during periods when the market has experienced a (large) drop in valuations. We also
document that liquidity commonality is positively related to market volatility but
unrelated to idiosyncratic volatility, indicating that inventory effects are not likely to be
the main source. In a follow-up to our paper, Comerton-Forde et al. (2008) provide
supportive evidence that capital constraints, proxied by higher inventory holdings by
NYSE specialists, lower market liquidity and are binding after negative market returns.4
We further find that while large negative return shocks to industry and market indices
increase commonality in liquidity, the market effect is larger in magnitude. These
findings suggest that spillover effects across all securities after negative market shocks
are important and provide strong support to the idea of a contagion in illiquidity due to
supply effects.
Next, using short-term price reversals as our measure of the return to supplying
liquidity, we examine if the cost of supplying liquidity depends on the state of market
returns. In Campbell, Grossman, and Wang (1993), risk-averse market makers require
payment for accommodating heavy selling by liquidity traders. This cost of providing
liquidity is reflected in the temporary decrease in price accompanying heavy sell volume
and the subsequent increase as prices revert to fundamental values. We use two return
reversal based trading strategies to empirically gauge the cost of supplying liquidity in
different market states: a zero-cost contrarian investment strategy (Avramov, Chordia,
7
Goyal (2006)) and a limit order trading strategy (Handa and Schwartz (1996)).5 The
zero-cost contrarian investment strategy that captures price reversals on heavy trading
yields an economically significant return of 1.18% per week when conditioned on large
negative market returns, and is much higher than the unconditional return of 0.58%. The
stronger price reversals in large down markets lasts up to two weeks, is higher in periods
of high liquidity commonality, and cannot be explained by standard Fama-French (1993)
risk factors. We obtain similar results using the limit order trading strategy. Overall, our
cumulative findings are consistent with the collateral-based view of liquidity put forward
in recent theoretical papers.
The remainder of the paper is organized as follows. Section I provides a description
of the data and key variables. The methodology and results on the relation between past
returns and liquidity are presented in Section II. Section III presents the empirical results
on the effect of market returns on commonality in liquidity. The findings from the
investment strategy based on short-term price reversals are produced in Section IV.
Section V concludes the paper.
I. Data
The transaction-level data are collected from the New York Stock Exchange Trades
and Automated Quotations (TAQ) and the Institute for the Study of Securities Markets
(ISSM). The daily and monthly return data are retrieved from the Center for Research in
Security Prices (CRSP). The sample stocks are restricted to NYSE ordinary stocks from
January 1988 to December 2003. We exclude NASDAQ stocks because their trading
protocols are different. ADRs, units, shares of beneficial interest, companies incorporated
8
outside the U.S., Americus Trust components, close-ended funds, preferred stocks, and
REITs are also excluded. In addition, to be included in our sample, the stock’s price must
be within $3 and $999 each year. This filter is applied to avoid the influence of extreme
price levels. The stock should also have at least 60 months of valid observations during
the sample period. After applying all the above filters, the final database includes more
than 800 million trades across about 1800 stocks over 16 years. The large sample enables
us to conduct a comprehensive analysis on the relations among liquidity level, liquidity
commonality, and market returns.
For the transaction data, if the trades are out of sequence, recorded before the
market open or after the market close, or with special settlement conditions, they are not
used. Quotes posted before the market open or after the market close are also discarded.
The sign of the trade is decided by the Lee and Ready (1991) algorithm, which matches a
trading record to the most recent quote preceding the trade by at least five seconds. If a
price is closer to the ask quote it is classified as a buyer-initiated trade, and if it is closer
to the bid quote it is classified as a seller-initiated trade. If the trade is at the midpoint of
the quote, we use a “tick-test” and classify it as buyer- (seller-) initiated trade if the price
is higher (lower) than the price of the previous trade. Anomalous transaction records are
deleted according to the following filtering rules: (i) negative bid-ask spread; (ii) quoted
spread > $5; (iii) proportional quoted spread > 20%; (iv) effective spread / quoted spread
> 4.0.
In this paper, we use bid-ask spread as our measure of liquidity. We compute the
proportional quoted spread (QSPR) by dividing the difference between ask and bid
quotes by the midquote. We repeat our empirical tests with the proportional effective
9
spread, which is two times the difference between the trade execution price and the
midquote scaled by the midquote, and find similar results (available in an Internet
Appendix6). The individual stock daily spread is constructed by averaging the spreads for
all transactions each day. During the last decade, spreads have narrowed with the
decrease in tick size and growth in trading volume. Thus, to ascertain the extent to which
the change in spread is caused by past returns, we adjust spreads for deterministic
time-series variation such as changes in tick-size, time trend, and calendar effects.
Following Chordia, Sarkar, and Subrahmanyam (2005), we regress stock i’s QSPR on
day s on a set of variables known to capture seasonal variation in liquidity:
,2121 ,,5,4,3,2
,1
11
1,,
4
1,,,
sisisisisi
sik
skkik
skkisi
ASPRYEARfYEARfTICKfTICKf
HOLIDAYfMONTHeDAYdQSPR
+++++
++= ∑∑== (1)
In equation (1), the following variables are employed: (i) day of the week dummies
(DAYk,s) for Monday through Thursday; (ii) month dummies (MONTHk,s) for January
through November; (iii) a dummy for trading days around holidays (HOLIDAYs); (iv) tick
change dummies TICK1s and TICK2s to capture the tick change from 1/8 to 1/16 on
06/24/1997 and the change from 1/16 to the decimal system on 01/29/2001, respectively;
and (v) time trend variables YEAR1s (YEAR2s), equal to the difference between the
current calendar year and 1988 (1997) or the first year when stock i started trading on
NYSE, whichever is later. The regression residuals, including the intercept, give the
adjusted proportional quoted spread (ASPR). The time-series regression equation is
estimated for each stock in our sample.
10
In results reported in the Internet Appendix, the cross-sectional average of the
estimated parameters show seasonal patterns in the quoted spread: the bid-ask spreads are
typically higher on Fridays and around holidays, and spreads are lower from May to
September relative to other months. The tick-size change dummies also pick up a
significant decrease in spreads after the change in tick rule on NYSE. These results
comport well with the seasonality in liquidity documented in Chordia, Sarkar, and
Subrahmanyam (2005). After adjusting for the seasonality in spreads, we do not observe
any significant time trend. In Table I, the unadjusted spread (QSPR) exhibits a clear time
trend with the annual average spread decreasing from 1.26% in 1988 to 0.26% in 2003,
but the trend is removed in the time series of the seasonally adjusted spread (ASPR)
annual averages. When plotting the two series, QSPR and ASPR, in Figure 1, we find
that our adjustment process does a reasonable job in controlling for the deterministic
time-series trend in stock spreads.
[Insert Table I and Figure 1 about here]
II. Liquidity and Past Returns
A. Time-series Analysis
We start our analyses by first aggregating the daily adjusted spreads for each stock to
obtain average weekly spreads. Denoting firm i’s adjusted proportional spread in week t
as ASPRi,t, we perform our analysis on changes in weekly spreads, (ASPRi,t minus
ASPRi,t-1 ) or ΔASPRi,t.7 We regress ΔASPRi,t on the lagged market return (Rm,t-1), proxied
by the CRSP value-weighted index. Since the exact horizon over which declines in
aggregate asset values affect liquidity is an empirical question, we examine the effect of
up to four lags of weekly returns.8 We test the key prediction of the underlying
11
theoretical models that liquidity is affected by lagged market returns, particularly,
negative returns. At the same time, it is possible that changes in liquidity are affected by
lagged firm-specific returns, since large changes in firm value may have similar wealth
effects. Firm i’s idiosyncratic returns (Ri,t) are defined as the difference between week t
returns on stock i and the market index.9
We introduce a set of firm-specific variables to control for other sources of
intertemporal variation in liquidity. Market microstructure models in Demsetz (1968),
Stoll (1978), and Ho and Stoll (1980) suggest that high volumes reduce inventory risk per
trade and thus should lead to smaller spreads. We add weekly changes in turnover
(ΔTURNit), measured by total trading volume divided by shares outstanding for firm i, to
control for the spread changes arising from the market maker’s inventory concerns.
Chordia, Roll, and Subrahmanyam (2002) report that order imbalances are correlated
with spreads and conjecture that this could arise because of the market maker’s difficulty
in adjusting quotes during periods of large order imbalances. To control for this effect,
we add changes in the relative order imbalance (ΔROIBit), measured by the change in
absolute value of the weekly difference in the dollar amount of buyer- and seller-initiated
orders standardized by the dollar amount of trading volume over the same period.
It is well known that bid-ask spreads are positively affected by return volatility due to
higher adverse selection and inventory risk (see, for example, Stoll (1978)). In the
volatility-return literature, a drop in stock prices increases financial leverage, which
makes the stock riskier and increases its subsequent volatility (see Black (1976) and
Christie (1982)). This implies that negative returns may increase spreads through their
impact on subsequent volatility. In Vayanos (2004), variation in demand for liquidity is
12
driven by changes in market volatility and during volatile periods increased risk aversion
leads to a flight to quality (here transactions costs are fixed over time). Vayanos (2004)
suggests that if transaction costs are higher during volatile times, the impact of volatility
on liquidity (premia) would be even stronger, emphasizing an important connection
between changes in market volatility and liquidity. We account for these volatility effects
by including contemporaneous and lagged changes in weekly volatility of market returns
(ΔSTDm,t) and volatility of stock i returns (ΔSTDi,t). Weekly volatility estimates are
obtained from daily returns over the previous four weeks using the method described in
French, Schwert, and Stambaugh (1987). Finally, we add lagged changes in spreads to
account for any serial correlations.
Weekly changes in adjusted spreads for each firm are regressed on weekly variables
as defined above:
,,4
1 ,,1,,61,51,4
1,3,2,14
1 ,,4
1 ,,,
tik ktikitiitiitii
tmitiitmik ktikik ktmkiiti
ASPRROIBcTURNcSTDc
STDcSTDcSTDcRRASPR
εφ
γβα
+Δ+Δ+Δ+Δ+
Δ+Δ+Δ+++=Δ
∑∑∑
= −−−−
−= −= − (2)
We run the time-series regression in equation (2) for each stock and report the mean and
median of the estimated regression coefficients across all firms in our sample, taking into
account the cross-equation correlations in the estimated parameters in computing the
standard errors.10 Table II presents the equally weighted average coefficients. Consistent
with previous literature, we find that a decrease in turnover or an increase in market and
idiosyncratic volatility predict higher spreads. Further, spreads increase when there is an
increase in contemporaneous or lagged volatility. The coefficient associated with changes
in order imbalance (ΔROIBit), on the other hand, has a positive value as expected, but is
statistically insignificant.
13
More importantly, we find that the lagged market returns in each of the past four
weeks affect current changes in spreads, with the effects declining rapidly as we move to
longer lags. Additionally, lagged idiosyncratic returns have a monotonically decreasing
and significant relation with current changes in adjusted spreads. Thus, consistent with
the theoretical predictions in Kyle and Xiong (2001), Brunnermeier and Pedersen (2009),
Garleanu and Pedersen (2007), and others, the wealth effect of a market wide drop in
asset prices is associated with a fall in liquidity.11
The models that link changes in market prices and liquidity actually pose a stronger
prediction: the relation should be stronger for prior losses than gains. Accordingly, we
modify equation (2) to allow spreads to react differentially to positive and negative
lagged returns:
,,4
1 ,,1,,61,51,4
1,3,2,14
1 ,,,,,
4
1 ,,4
1 ,,,,,4
1 ,,,
tik ktikitiitiitii
tmitiitmik ktiDOWNktikiDOWN
k ktikik ktmDOWNktmkiDOWNk ktmkiiti
ASPRROIBcTURNcSTDc
STDcSTDcSTDcDR
RDRRASPR
εφ
γ
γββα
+Δ+Δ+Δ+Δ
+Δ+Δ+Δ++
+++=Δ
∑∑
∑∑∑
= −−−−
−= −−
= −= −−= −
(3)
where DDOWN,m,t (DDOWN,i,t ) is a dummy variable that is equal to one if and only if Rm,t
(Ri,t) is less than zero. The control variables are identical to those defined in equation (2).
In Panel B of Table II, we find a significantly greater effect of negative market
returns on liquidity: the regression coefficient on lagged market returns in week t-1 rises
significantly from -0.413 to -1.223 when the market return is negative. Spreads are also
asymmetrically related to lagged idiosyncratic returns, although the magnitude of the
asymmetry is less dramatic, with the regression coefficient changing from -0.473 to
-0.631. Interestingly, the sharp increase in spreads in week t-1, due to negative market
14
returns, reverses to its mean in weeks t-3 and t-4, indicating that the liquidity effects last
up to two weeks.
[Insert Table II about here]
To examine whether the magnitude of lagged returns has any material impact on
liquidity, the regression specification is
,,4
1 ,,1,,61,51,4
1,3,2,1
4
1 ,,,,,4
1 ,,,,,
4
1 ,,4
1 ,,,,,
4
1 ,,,,,4
1 ,,,
tik ktikitiitiitii
tmitiitmi
k ktiLARGEUPktikiLARGEUPk ktiLARGEDOWNktikiLARGEDOWN
k ktikik ktmLARGEUPktmkiLARGEUP
k ktmLARGEDOWNktmkiLARGEDOWNk ktmkiiti
ASPRROIBcTURNcSTDc
STDcSTDcSTDc
DRDR
RDR
DRRASPR
εφ
γγ
γβ
ββα
+Δ+Δ+Δ+Δ
+Δ+Δ+Δ+
++
++
++=Δ
∑
∑∑∑∑
∑∑
= −−−−
−
= −−= −−
= −= −−
= −−= −
(4)
where DDOWN LARGE,m,t (DUP LARGE,m,t ) is a dummy variable that is equal to one if and only
if Rm,t is more than 1.5 standard deviations below (above) its unconditional mean return.
Similarly, DDOWN LARGE,i,t (DUP LARGE,i,t ) is a dummy variable that is equal to one if and
only if Ri,t is more than 1.5 standard deviations below (above) its mean return.12
In Table II, Panel C, large negative market shocks significantly widen the bid-ask
spreads while large positive market returns have an insignificant marginal effect,
reinforcing the striking asymmetric effect of market returns on liquidity. Our findings add
to those in Chordia, Roll, and Subrahmanyam (2001, 2002), who show that at the
aggregate level, daily spreads increase dramatically following days with negative market
returns but decrease only marginally on positive market daily returns. Consistent with the
results in Panel B, the increase in spreads following large negative market returns in
week t-1 reverses at longer lags.
Additional analyses available in the Internet Appendix provide more insights. First,
we find a significant increase in adjusted spreads of 2.8 (6.2) basis points following a
15
(large) negative market return in week t-1, after controlling for other determinants of
spreads. Second, Deuskar (2007) presents a model where an increase in investors’
perceived asset risk reduces current prices and makes the market more illiquid. In her
model, higher forecasts of volatility affect investor sentiment and hence realized volatility
and liquidity. Specifically, her model predicts lowers liquidity when misperceived
volatility, measured by the difference between implied volatility of S&P 100 index
options (VIX) and realized index volatility, is higher. Consistent with Dueskar (2007), we
find that changes in weekly adjusted spread are significantly and positively related to
contemporaneous and lagged misperceived weekly volatility. However, the misperceived
volatility effects do not displace the strong negative influence of lagged returns.13
Moreover, adding more lags of volatility does not affect our results, indicating that the
intertemporal influence of volatility is different from the return effects. Hence, our
evidence on lower liquidity following a decrease in aggregate market value of securities
is robust.
B. Evidence on the Effects of Funding Constraints
We interpret the relation between market declines and liquidity dry-ups as indicative
of capital constraints in the marketplace. A direct test of this supply-side explanation
requires that we identify independent changes in funding liquidity at weekly frequencies.
Although we do not have access to direct measures of aggregate supply shocks, we use
indirect measures from the financial sector to investigate if the contraction in liquidity is
consistent with liquidity providers becoming more capital constrained. With equation (3)
as a starting point, we examine if the sensitivity of changes in spreads to negative market
16
returns differs during periods when the suppliers of liquidity are likely to face capital
tightness. The following regression model is estimated:
,,4
1 ,,1,,61,51,4
1,3,2,14
1 ,,,,,
4
1 ,,1,1,,1,,,,
4
1 ,,,,,4
1 ,,,
tik ktikitiitiitii
tmitiitmik ktiDOWNktikiDOWN
k ktikitCAPtmDOWNtmkiCAPDOWN
k ktmDOWNktmkiDOWNk ktmkiiti
ASPRROIBcTURNcSTDc
STDcSTDcSTDcDR
RDDR
DRRASPR
εφ
γ
γβ
ββα
+Δ+Δ+Δ+Δ
+Δ+Δ+Δ++
++
++=Δ
∑∑
∑∑∑
= −−−−
−= −−
= −−−−
= −−= −
(5)
where DCAP,t is a dummy variable that takes a value of one only if week t is associated
with periods of higher capital constraints.
We use three proxies to capture tightness of capital in the market. The first proxy is
based on the (value-weighted) return on the portfolio of investment banks and securities
brokers and dealers listed on NYSE, defined by SIC code 6211.14 We compute the
excess returns on the portfolio of stocks in the investment banking sector by the residuals
from a one-factor market model regression. A large fall in the market value of the firms
operating in investment banking and securities brokerage services is likely to reflect a
weak aggregate balance sheet of the funding sector. Hence, when the excess returns on
this portfolio of financial intermediaries are negative in week t, DCAP,t is set to one.15
Adrian and Shin (2008) show that the financial intermediaries adjust their leverage in
a procyclical manner, with expansion and contraction of their balance sheets effected
through repos. For example, when financial intermediaries have weak balance sheets,
their leverage is too high. The ensuing capital shortage forces the intermediaries to
contract their balance sheets.16 Adrian and Shin show that these changes in aggregate
intermediary balance sheets are linked to funding liquidity through shifts in market wide
risk appetite. We therefore use the weekly changes in aggregate repos as our second
17
measure of constraints in the funding market and set DCAP,t to one when there is a decline
in aggregate repos in week t.17
Our third measure of funding liquidity relies on the weekly spread in commercial
paper (CP), measured as the difference in the weekly returns on the three-month
commercial paper rate and three-month Treasury bill rate.18 It is well known that the CP
market is very illiquid. As Krishnamurthy (2002) shows, the difference in the return on
CP and T-bills (or the CP spread) reflects a liquidity premium demanded by the large
investors in CP such as money market mutual funds and other financial corporations.
Gatev and Strahan (2006) use the CP spread to measure liquidity supply and show that
the spread widens during liquidity events. Since changes in CP spreads are related to the
willingness of these intermediaries to provide liquidity, we argue that an increase in the
weekly CP spread is likely to be associated with a period when the funding market is
capital constrained. Hence, DCAP,t is equal to one when there is an increase in the CP
spread in week t.
Panel A of Table III shows that a decline in aggregate market valuations leads to a
significantly greater increase in bid-ask spreads when there is also an underperformance
in the investment banking and brokerage sector.19 In Panel B, a contraction in the
balance sheet of the financial intermediaries, measured by a decrease in repos, has a
similar effect. To be precise, a negative return on the market index in week t-1 lowers the
regression coefficient for market returns from -0.43 to -0.95. A simultaneous decrease in
aggregate repos in the capital markets magnifies the impact of negative market returns to
-1.63. Finally, our findings are reinforced by a similar amplification of the effect of
negative market returns in Panel C, following an increase in CP spreads. Together, the
18
evidence in Table III is strongly supportive of our interpretation that liquidity dry-ups
following market declines are related to tightness in funding liquidity.
[Insert Table III about here]
C. Cross-sectional Evidence
The theoretical models in Brunnermeier and Pedersen (2009) and Garleanu and
Pedersen (2007) suggest that high volatility stocks require greater use of risk capital and
are more likely to suffer higher haircuts (margin requirements) when funding constraints
bind. Consequently, a drop in funding liquidity (large negative market return shock)
increases the differential liquidity between high and low volatility securities.
In this subsection, we examine the cross-sectional differences in the relation between
lagged returns and spreads among stocks that differ in volatility, controlling for firm size.
Firms are sorted into nine size-volatility portfolios based on two-way dependent sorts on
each firm’s beginning-of-year market capitalization and its return volatility in the
previous year, and the portfolio composition is rebalanced each year. In each week t, we
average the adjusted spreads on each firm to produce nine portfolio-level spreads,
ASPRp,t. Similar to the firm-specific variables defined in equation (3), for each week t, we
average the relative order imbalance across all firms in each portfolio, denoted as ROIBp,t,
and calculate portfolio turnover, TURNp,t, portfolio-specific returns (Rp,t) and volatility,
STDp,t. We regress the change in spreads at the portfolio level on changes in the control
variables as well as portfolio and market returns, analogous to equation (3), but for
portfolio p, where p=1,2,…,9:
19
,,4
1 ,,1,,61,51,4
1,3,2,14
1 ,,,,,
4
1 ,,4
1 ,,,,,4
1 ,,,
tpk ktpkptpptpptpp
tmptpptmpk ktpDOWNktpkpDOWN
k ktpkpk ktmDOWNktmkpDOWNk ktmkpitp
ASPRROIBcTURNcSTDc
STDcSTDcSTDcDR
RDRRASPR
εφ
γ
γββα
+Δ+Δ+Δ+Δ
+Δ+Δ+Δ++
+++=Δ
∑∑
∑∑∑
= −−−−
−= −−
= −= −−= −
(6)
The system of equations in (6) is estimated using the seemingly unrelated regression
(SUR) method, allowing for cross-equation correlations. Consistent with the results in
Table II, Table IV shows that changes in spreads are negatively related to market returns,
controlling for portfolio-specific factors. The sensitivity of spreads to market returns is
larger for high volatility portfolios, particularly during market downturns. These sharp
increases in spreads reverse in subsequent weeks, revealing the short-run nature of the
phenomenon. Our results are not a manifestation of size-related effects since we find
analogous results within each of the size thirtiles. The reaction of spreads to own-
portfolio negative returns are less dramatic, however. Hence, less liquidity is available for
high volatility stocks when the liquidation of these assets (collateral) becomes more
costly, consistent with a flight to liquidity.
[Insert Table IV about here]
It is interesting to note that the impact of negative market returns on liquidity is in the
same direction for each of the nine size-volatility portfolios, suggesting a high
commonality in liquidity, an issue that we investigate further in the next section.
III. Commonality in Liquidity
A. Commonality in Liquidity and Market Returns
When market makers and other intermediaries are constrained by their capital base, a
large negative return reduces the pool of capital that is tied to marketable securities and
20
hence reduces the supply of liquidity. The theoretical model in Brunnermeier and
Pedersen (2009), for example, predicts that the funding liquidity constraints increase the
commonality in liquidity across securities. In a recent paper, Kamara, Lou, and Sadka
(2008) find that liquidity betas change over time and that these changes are affected by
market volatility as well as market returns.
We start with an investigation of the impact of market returns on a firm’s liquidity
beta, using the regression framework in (3). We do this by introducing a measure of
weekly market adjusted spreads, ASPRm,t, which is obtained by averaging the firm-level
adjusted spreads, NASPRN
i ti /)(1 ,∑ =
. The weekly change in market spreads (ASPRm,t
-ASPRm,t-1) is denoted as ΔASPRm,t and the sensitivity of firm i’s spread to ΔASPRm,t is its
liquidity beta, bLIQ,i.
tik ktikitiitiitii
tmitiitmik ktiDOWNktikiDOWN
k ktikik ktmDOWNktmkiDOWNk ktmki
tmDOWNtmiDOWNLIQtmiLIQiti
ASPRROIBcTURNcSTDc
STDcSTDcSTDcDR
RDRR
DASPRbASPRbASPR
,4
1 ,,1,,61,51,4
1,3,2,14
1 ,,,,,
4
1 ,,4
1 ,,,,,4
1 ,,
,,,,,,,,
εφ
γ
γββ
α
+Δ+Δ+Δ+Δ
+Δ+Δ+Δ++
+++
Δ+Δ+=Δ
∑∑
∑∑∑
= −−−−
−= −−
= −= −−= − (7)
.,4
1 ,,1,,61,51,4
1,3,2,14
1 ,,,,,
4
1 ,,4
1 ,,,,,4
1 ,,
,,,,,
,,,,,,,,
tik ktikitiitiitii
tmitiitmik ktiDOWNktikiDOWN
k ktikik ktmDOWNktmkiDOWNk ktmki
tmLARGEDOWNtmiLARGEDOWNLIQ
tmSMALLDOWNtmiSMALLDOWNLIQtmiLIQiti
ASPRROIBcTURNcSTDc
STDcSTDcSTDcDR
RDRR
DASPRb
DASPRbASPRbASPR
εφ
γ
γββ
α
+Δ+Δ+Δ+Δ
+Δ+Δ+Δ++
+++
Δ+
Δ+Δ+=Δ
∑∑
∑∑∑
= −−−−
−= −−
= −= −−= − (8)
It should be noted that we exclude firm i in the computation of market spreads.
Although changes in liquidity levels are different from liquidity commonality, it is
possible that they are correlated. For example, if low market returns predict low liquidity
21
for all stocks, then liquidity covariance with aggregate liquidity may increase following
low market returns. Hence, we test for both liquidity level and commonality effects in
equation (7). Specifically, we examine whether bLIQ,i changes during periods of negative
market returns, as captured by bLIQ,DOWN,i . In equation (8) we also investigate whether
bLIQ,i changes when market returns are negative and small (bLIQ,DOWN,SMALL,i) or negative
and large (bLIQ,DOWN,LARGE,i), where small (large) is defined as negative market returns that
are less (more) than 1.5 standard deviations below the unconditional mean market
returns.
Consistent with the findings in Kamara, Lou, and Sadka (2008), Panel A of Table V
shows that bLIQ,i increases significantly from 0.56 to 0.87 in down market states. In Panel
B, the largest increase in liquidity commonality happens during large market downturns,
when bLIQ,i increases to 0.95. Moreover, the asymmetric effect of market returns on
spreads documented in Section II persists after accounting for changes in liquidity
commonality. Hence, the results in Table V emphasize two separate effects: an increase
in illiquidity levels as well as commonality in response to market downturns.
[Insert Table V about here]
We also investigate the effect of market returns on commonality in liquidity using an
alternate metric that captures comovement. The R2 statistic from the market model
regression has been extensively used to measure comovement in stock prices (e.g., Roll
(1988), Morck, Yueng, and Yu (2000)). We follow Chordia, Roll, and Subrahmanyam
(2000) and use a single-factor market model to compute the commonality in liquidity.
Changes in daily adjusted proportional spreads for firm i on day s (ΔASPRi,s) are
regressed on changes in daily market average adjusted spreads (ΔASPRm,s):
22
.,,,, sismiLIQisi ASPRbaASPR ε+Δ+=Δ (9)
For each stock i with at least 15 valid daily observations in month t, the market model
regression yields a regression R2 denoted as R2i,t. A high R2
i,t indicates that a large portion
of the variation in liquidity for stock i in month t is due to common, market wide liquidity
movements. For each month t, the strength of liquidity commonality is measured by
taking an equally weighted average of R2i,t, denoted as R2
t.
Figure 2 shows significant time-series variation in liquidity commonality, R2t, over
the sample period 1988 to 2003. We observe spikes in liquidity commonality associated
with periods of liquidity crisis. For example, the highest levels of commonality in
liquidity in Figure 2 coincide with liquidity dry-ups during the Asian financial crisis
(1997), LTCM crisis (1998), and September 11, 2001 terrorist attacks. These periods are
also accompanied by large negative market returns, highlighting the episodic nature of
illiquidity. The average liquidity R2 increases to 10.1% in large negative market returns
states, compared to 7.4% when market returns are positive. In results available in the
Internet Appendix, the dynamic conditional correlations (DCC) methodology introduced
by Engle (2002) yields supportive findings: the conditional correlations in illiquidity
(spreads) among size-sorted portfolios are significantly higher following large market
declines. We also find a similar increase in the conditional correlation between two
portfolios of stocks constructed based on whether the stock is an S&P 500 index stock or
not. The latter result suggests that the common variation in liquidity cannot be fully
explained by demand for liquidity by index-linked funds or index arbitrageurs (see
23
Harford and Kaul (2005)). Our results underscore the main idea that illiquidity becomes
more correlated across all assets following market declines.
[Insert Figure 2 about here]
The intertemporal variation in liquidity commonality may also be affected by factors
related to changes in demand for liquidity. In Vayanos (2004), investors become more
risk averse and their preference for liquidity increases in volatile times. Consequently, a
jump in market volatility, the main state variable in his model, is associated with higher
demand for liquidity and conceivably increases liquidity commonality. Extreme
aggregate imbalances in the buyer- and seller-initiated orders for securities may increase
the demand for liquidity as shown by Chordia, Roll, and Subrahmnayam (2002). If high
levels of aggregate order imbalance impose similar pressure across securities, they are
also likely to increase commonality in spreads. In addition, correlated shifts in demand by
buyer- or seller-initiated trades would lead to commonality in order imbalances. Hence,
we explore the impact of both the level and commonality in order imbalances on liquidity
commonality. The level of order imbalances (ROIB) is defined above in Section II. To
measure commonality in order imbalances (ROIBCOM), we estimate the R2 from a
regression of individual firm order imbalances on market (equally weighted average)
order imbalances, similar in spirit to the liquidity commonality measure using
proportional spreads in equation (9).
We introduce these additional variables that may affect liquidity commonality within
a regression framework. Since the R2t values are constrained to be between zero and one
by construction, we define liquidity comovement as the logit transformation of R2t,
LIQCOMt = ln[R2t /(1−R2
t)]. We regress our comovement measure on the above variables
24
as well as market returns (Rmt), taking into account the sign and magnitude of market
returns:
,32,1,,
,,,
ttttmtLARGEUPtmLARGEUP
tLARGEDOWNtmLARGEDOWNtmt
ROIBCOMcROIBcSTDcDR
DRRaLIQCOM
εβ
ββ
+++++
++= (10)
where the return and dummy variables are defined in equation (4).
As shown in Table VI, liquidity comovement is strongest when there is a large drop
in aggregate market prices. Shifts in the order imbalance comovement, which we
interpret as a measure of correlation in demand for liquidity, are positively associated
with liquidity commonality. The level of aggregate order imbalance (ROIB) also
positively affects liquidity commonality. Consistent with the prediction in Vayonas
(2004), uncertainty in the market (STDm,t) increases investor demand for liquidity and
subsequently increases liquidity commonality. Nevertheless, adding these measures of
demand effects does not eliminate the significant asymmetric effect of market returns on
liquidity commonality.
To the extent that comovement in order imbalances across securities picks up
correlation in demand for liquidity, it would be interesting to document the sources that
drive the common variations in order flow. We consider one more explanatory variable:
monthly net flow of funds into U.S. equity mutual funds for our sample period from 1988
to 2003. We divide the net fund flow data from Investment Company Institute by the total
assets under management by U.S. equity funds to generate our monthly time series of net
mutual fund flow. When there is a large withdrawal of money by mutual fund owners in
aggregate, fund managers are less willing and able to hold (particularly illiquid) assets,
creating correlated demand for liquidity across stocks.
25
As reported in column (4) of Table VI, order imbalance comovement increases with
market volatility and is negatively related to net mutual fund flows, corresponding to
changes in demand for liquidity. Unlike the evidence on liquidity commonality, order
imbalances across stocks decrease after a large decline in market valuations. The latter
result is not surprising since market returns and constraints on aggregate capital are not
expected to affect liquidity demand in the same way.
[Insert Table VI about here]
The positive correlation between the two comovement measures suggests that these
variables may affect each other simultaneously. To address this endogeneity problem, we
re-estimate the coefficients based on two-stage least squares (2SLS) estimation, using net
mutual fund flow and lagged order imbalance comovement to identify the demand
(commonality in order imbalance) equation. As shown in the last two columns of Table
VI, our finding that liquidity commonality increases in large down market states is
robust.
Overall, the results show that while liquidity commonality is driven by changes in
supply as well as demand for liquidity, the demand factors cannot explain the asymmetric
effect of market returns on liquidity. On the other hand, the increase in liquidity
commonality in down market states is consistent with the adverse effects of a decrease in
the supply of liquidity.
B. Industry Spillover Effects
Virtually all the theoretical models, including Kyle and Xiong (2001), Gromb and
Vayanos (2002), Brunnermeier and Pedersen (2009), and Garnealu and Pedersen (2007),
26
suggest a contagion in illiquidity. We broaden our investigation by addressing whether
industry-wide comovement in liquidity is affected by a decrease in the valuation of stocks
from other industries, over and above the effect of own-industry portfolio returns. If
commonality in liquidity is driven by capital constraints faced by the market making
sector in supplying liquidity, we should observe correlated illiquidity within an industry
increase with a decline in the market values of securities in other industries.
We begin by estimating in each month the following industry factor model for daily
changes in spreads for security i (ΔASPRi,s):
,,,,, sisINDjiLIQisi ASPRbaASPR ε+Δ+=Δ (11)
where the industry liquidity factor (ΔASPRINDj,s) is the daily change in the equally
weighted average of adjusted spreads across all stocks in industry j on day s. Similar to
our approach in equation (9), we average the regression R2 from equation (11) for each
month t, across all firms in industry j. To obtain an industry-wide measure of
commonality in liquidity for each month t, we perform a logit transformation of the
industry average R2, denoted as LIQCOMINDj,t. We form 17 industry-wide comovement
measures using the SIC classification derived by Fama and French, which is provided by
Kenneth French’s online data library.20 LIQCOMINDj,t, is regressed on the monthly
returns on the industry portfolio j (RINDj,t) and the returns on the market portfolio,
excluding portfolio j (RMKTj,t), taking into account the sign and magnitude of these
returns:
ttMKTjDOWNtMKTjDOWNtMKTj
tINDjDOWNtINDjDOWNtINDjtINDj
DRR
DRRaLIQCOM
εββ
δδ
+++
++=
,,,,
,,,,, (12)
27
,,,,,,,,
,,,,,,,,
ttMKTjLARGEUPtMKTjLARGEUPtMKTjLARGEDOWNtMKTjLARGEDOWNtMKTj
tINDjLARGEUPtINDjLARGEUPtINDjLARGEDOWNtINDjLARGEDOWNtINDjtINDj
DRDRR
DRDRRaLIQCOM
εβββ
δδδ
++++
+++= (13)
where the dummy variables are defined in the same way as in equations (3) and (4). The
regression coefficient associated with the independent variable tMKTjR , measures
liquidity spillover effects.
As presented in Table VII, we find that the returns on the market portfolio (i.e., the
portfolio of securities in other industries, excluding own industry) exert a strong
influence on comovement in liquidity within the industry, especially when the market
returns are negative. In fact, the market portfolio returns dominate the industry returns in
terms of the effect on industry-wide liquidity movements. The regression coefficient
estimate on negative market returns is a significant -1.995 while the coefficient on
negative industry returns is smaller at -0.986. When we separate the returns according to
their magnitude, large negative market returns turn out to have the greatest impact on
industry-level liquidity movements. In Table VII, we also obtain similar spillover effects
of market wide returns when we replace LIQCOMINDj,t with the industry average liquidity
betas, bLIQ,t (defined in equation (11)). These results strongly support the idea that when
large negative market returns occur, spillovers due to capital constraints extend across
industries, increasing the commonality in liquidity.
[Insert Table VII about here]
IV. Liquidity and Short-term Price Reversals
In Campbell, Grossman, and Wang (1993), risk-averse market makers require
compensation for supplying liquidity to meet fluctuations in aggregate demand for
28
liquidity. This cost of providing liquidity is reflected in the temporary decrease in prices
accompanying heavy sell volume and the subsequent increase as prices revert to
fundamental values.21 Conrad, Hameed, and Niden (1994), Avramov, Chordia, and
Goyal (2006), and Kaniel, Saar, and Titman (2008) provide empirical support for the
relation between short-term price reversals and illiquidity and show that high volume
stocks exhibit significant weekly return reversals. According to the collateral-based
models discussed earlier, the return reversals should be stronger following market
declines.
We examine the extent of price reversals in different market states using two
empirical trading strategies, namely, contrarian and limit order trading strategies. The
first strategy relies on the formulation in Avramov, Chordia, and Goyal (2006). We
construct Wednesday to Tuesday weekly returns for all NYSE stocks in our sample for
the period 1988 to 2003. Skipping one day between two consecutive weeks avoids the
potential negative serial correlation caused by the bid-ask bounce and other
microstructure influences. Next, we sort the stocks in week t into positive and negative
return portfolios. For each week t, returns on stock i (Rit) that are higher (lower) than the
median return in the positive (negative) return portfolio are classified as winner (loser)
securities. We use stock i’s turnover in week t (Turnit) to measure the amount of trading.
The contrarian portfolio weight of stock i in week t+1 within the winner and loser
portfolios is given by ∑ =+ −=Npt
i tititititpi TurnRTurnRw1 ,,,,1,, / , where Npt denotes the
number of securities in the loser or winner portfolios in week t. The contrarian
investment strategy is long on the loser securities and short on the winner securities. The
29
contrarian profits for the loser and winner portfolios for week t+k are:
∑ = +++ =Np
i ktitpiktp Rw1 ,1,,,π , which can be interpreted as the return to a $1 investment in
each portfolio. The zero-investment profits are obtained by taking the difference in
profits from the loser and winner portfolios.
We investigate the effect of lagged market returns by conditioning the contrarian
profits on cumulative market returns over the previous four weeks. Specifically, we
examine contrarian profits in four market states: large up (down) markets defined as
market return being more than 1.5 standard deviations above (below) the mean return;
and small up (down) markets, defined as market returns between zero and 1.5 (-1.5)
standard deviations around the mean return.
In the second trading strategy, we follow Handa and Schwartz (1996) and devise a
simple limit order trading rule to measure the profits to supplying liquidity.22 When a
limit buy order is submitted below the prevailing bid price, the limit order trader provides
liquidity to the market. If price variations are due to short-term selling pressure, the limit
buy order will be executed and we should observe subsequent price reversals, reflecting
compensation for liquidity provision. At the same time, the limit order trader expects to
lose from the trade upon arrival of informed traders, in which case the price drop would
be permanent (i.e., a limit buy order imbeds a free put option).
The limit order strategy is implemented as follows. At the beginning of each week t,
a limit buy order is placed at x% below the opening price (Po). We consider three values
of x: 3%, 5%, and 7%. If the transaction price falls to Po (1- x%) or below within week t,
the limit order is executed and the investment is held for a period of k weeks (k = 1 and
30
2). If the limit order is not executed in week t, we assume that the order is withdrawn. A
similar strategy is employed to execute limit sell orders if prices reach or exceed Po (1+
x%). For the week t+1, we construct the cross-sectional average weekly returns (for buy
and sell orders), weighting each stock i by its turnover in week t
∑ =+ =Npt
i tititi TurnTurnw1 ,,1, / . Again, we investigate whether the payoff to the limit
order trading strategy varies across market states.
Table VIII, Panel A reports a significant contrarian profit of 0.58% in week t+1
(t-statistic=5.38) for the full sample period. The contrarian profit declines rapidly and
becomes insignificant as we move to longer lags. Since the contrarian profits and price
reversals appear to last for at most two weeks, we limit our subsequent analyses to the
first two weeks after portfolio formation. Panel B of Table VIII shows that the largest
contrarian profit is registered in the period following a large decline in market prices.
Week t+1 profits in the large down market increase noticeably to 1.18% compared to
profits of between 0.52% and 0.64% in other market states. We find a similar profit
pattern in week t+2, although the magnitude falls quickly. It is worth noting that the loser
portfolio shows the largest profit (above 1.0% per week) following large negative market
returns.
To ascertain whether the difference in loser and winner portfolio returns can be
explained by loadings on risk factors, we estimate the alphas from a Fama-French
three-factor model. We regress the contrarian profits on market (return on the
value-weighted market index), size (difference in returns on small and large market
capitalization portfolios), and book-to-market (difference in returns on value and growth
portfolios) factors. 23 The risk-adjusted profits in large down markets remain
31
economically large at 1.16% per week, indicating that these risk factors cannot explain
the price reversals. In results available in the Internet Appendix, we find that the
contrarian profits jump to 1.73% following periods of high liquidity commonality (as
defined in Section III) and large market declines.
[Insert Table VIII about here]
Table IX, Panel A shows that our limit order trading strategy generates significant
profits for all three discount values, that is, 3%, 5% and 7%, with weekly buy-minus-sell
portfolio returns ranging from 0.37% to 0.97% in the first week. These returns become
economically small in magnitude beyond one week. In Panel B, the buy-minus-sell
portfolio returns are similar in all the market states, except for large down states. For
example, the 5% limit order trading rule generates buy-minus-sell returns of between
0.63% and 0.68% per week in most market states. The striking exception is in large down
markets, where the portfolio returns more than double to 1.56%.
[Insert Table IX about here]
Hence, the evidence from both strategies shows that the compensation for supplying
liquidity increases in large down markets, indicative of supply effects in equity markets
arising from tightness in capital.
V. Conclusion
This paper documents that liquidity responds asymmetrically to changes in asset
market values. Consistent with theoretical models emphasizing changes in the supply of
liquidity, negative market returns decrease liquidity much more than positive returns
increase liquidity, with the effect being strongest for high volatility firms and during
times when the market making sector is likely to face capital tightness. We show a drastic
32
increase in commonality in liquidity after large negative market returns, and peaks in the
commonality measure coincide with periods often associated with liquidity crisis. Hence,
market declines affect both liquidity level and liquidity commonality. We also document
that liquidity commonality within an industry increases significantly when the returns on
other industries (excluding the specific industry) are large and negative, suggesting
contagion in illiquidity: illiquidity in one industry spills over to other industries.
The contagion in illiquidity and increase in liquidity commonality as aggregate asset
values decline provide indirect evidence of a drop in the supply of liquidity affecting all
securities. We argue that demand effects, such as buy-sell order imbalances, cannot fully
explain our results. Finally, we use the idea that short-term stock price reversals
following heavy trading reflect compensation for supplying liquidity and examine
whether the cost of liquidity provision varies with large changes in aggregate asset
values. We find that, indeed, the cost of providing liquidity is highest in periods with
large market declines and high commonality in liquidity. For example, contrarian or limit
order trading strategies based on return reversals produce economically significant
returns (between 1.18% and 1.56% per week) after a large decline in aggregate market
prices. Taken together, our results support a supply effect on liquidity as advocated by
Kyle and Xiong (2001), Gromb and Vayanos (2002), Anshuman and Viswanathan
(2005), Brunnermeier and Pedersen (2009), Garleanu and Pedersen (2007), and Mitchell,
Pedersen, and Pulvino (2007). Further, our empirical results indicate that the illiquidity
effect in the equity market lasts between one to two weeks, on average. We interpret our
results as suggesting the presence of supply effects even in liquid markets like U.S.
equities with capital flowing into the market fairly quickly.
33
Overall, our paper presents evidence supportive of the collateral view of market
liquidity: market liquidity drops after large negative market returns because aggregate
collateral of financial intermediaries falls and many asset holders are forced to liquidate,
making it difficult to provide liquidity precisely when the market needs it. However, our
evidence is indirect. A fruitful avenue for future research would be to investigate the
effect of funding constraints using high frequency data on the balance sheet positions
held by intermediaries.
34
REFERENCES
Acharya, Viral V., and Lasse Heje Pedersen, 2005, Asset pricing with liquidity risk, Journal of Financial Economics 77, 375-410.
Adrian, Tobias, and Hyun Song Shin, 2008, Liquidity and leverage, Working paper, Princeton University.
Allen, Franklin, and Douglas Gale, 2005, From cash-in-the-market pricing to financial fragility, Journal of European Economic Association 3, 535-546.
Amihud, Yakov, and Haim Mendelson, 1986, Asset pricing and the bid-ask spread, Journal of Financial Economics 17, 223-249.
Ang, Andrew, and Joe Chen, 2002, Asymmetric correlations in equity portfolios, Journal of Financial Economics 63, 443-494.
Ang, Andrew, Joe Chen, and Yuhang Xing, 2006, Downside risk, Review of Financial Studies 19, 1191-1239.
Anshuman, Ravi and S. Viswanathan, 2005, Costly collateral and liquidity, Working paper, Duke University.
Avramov, Doron, Tarun Chordia, and Amit Goyal, 2006, Liquidity and autocorrelation of individual stock returns, Journal of Finance 61, 2365-2394.
Baker, Malcolm and Jeremy C. Stein, 2004, Market liquidity as a sentiment indicator, Journal of Financial Markets 7, 271-299.
Barber, Brad, Terrance Odean, and Ning Zhu, 2008, Do noise traders move markets? Review of Financial Studies, forthcoming.
Bernado, Antonio, and Ivo Welch, 2003, Liquidity and financial market runs, Quarterly Journal of Economics 119, 135-158.
Black, F., 1976, Studies of stock price volatility changes, Proceedings of the 1976 Meetings of the Business and Economics Statistics Section, American Statistical Association, 177-181.
Brunnermeier, Markus and Lasse Pedersen, 2009, Market liquidity and funding liquidity, Review of Financial Studies 22, 2201-2238.
Campbell, John Y., Sanford J. Grossman, and Jiang Wang, 1993, Trading volume and serial correlation in stock returns, Quarterly Journal of Economics, 108, 905-939.
Chordia, Tarun, Richard Roll, and Avanidhar Subrahmanyam, 2000, Commonality in liquidity, Journal of Financial Economics 56, 3-28.
35
Chordia, Tarun, Richard Roll, and Avanidhar Subrahmanyam, 2001, Market liquidity and trading activity, Journal of Finance 56, 501-530.
Chordia, Tarun, Richard Roll, and Avanidhar Subrahmanyam, 2002, Order imbalance, liquidity and market returns, Journal of Financial Economics 65, 111-130.
Chordia, Tarun, Asani Sarkar, and Avanidhar Subrahmanyam, 2005, An empirical analysis of stock and bond market liquidity, Review of Financial Studies 18, 85-129.
Christie, Andrew A., 1982, The stochastic behavior of common stock variances: Value, leverage and interest rate effect, Journal of Financial Economics 10, 407-432.
Comerton-Forde, Carole, Terence Hendershott, Charles Jones, Pamela Moulton, and Mark Seasholes, 2008, Time variation in liquidity: The role of market maker inventories and revenues, Working paper, UC-Berkeley.
Conrad, Jennifer, Allaudeen Hameed, and Cathy Niden, 1994, Volume and autocovariances in short-horizon individual security returns, Journal of Finance 49, 1305-1329.
Coughenour, Jay, and Mohsen Saad, 2004, Common market makers and commonality in liquidity, Journal of Financial Economics 73, 37-69.
Demsetz, Harold, 1968, The cost of transaction, Quarterly Journal of Economics 82, 33-53.
Dueskar, Prachi, 2007, Extrapolative expectations: Implications for volatility and liquidity, Working paper, University of Illinois at Urbana-Champaign.
Eisfeldt, Andrea, 2004, Endogenous liquidity in asset markets, Journal of Finance 59, 1-30.
Engle, Robert, 2002, Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models, Journal of Business & Economic Statistics 20, 339-350.
Fama, Eugene F. and Kenneth R. French, 1993, Common risk factors in the return on stocks and bonds, Journal of Financial Economics 33, 3-56.
French, Kenneth, G. William Schwert, and Robert Stambaugh, 1987, Expected stock returns and volatility, Journal of Financial Economics 19, 3-29.
Garleanu, Nicolae, and Lasse Heje Pedersen, 2007, Liquidity and Risk Management, American Economic Review 97, 193-197.
36
Gatev, Evan, and Philip E. Strahan, 2006, Banks Advantage in Hedging Liquidity Risk: Theory and Evidence from the Commercial Paper Market, Journal of Finance 61, 867-892
Gervais, Simon, and Terrance Odean, 2001, Learning to be Overconfident, Review of Financial Studies 14, 1-27.
Gromb, Denis, and Dimitri Vayanos, 2002, Equilibrium and Welfare in Markets with Financially Constraint Arbitrageurs, Journal of Financial Economics 66, 361-407.
Handa, Puneet, and Robert A. Schwartz, 1996, Limit order trading, Journal of Finance 51, 1835-1861.
Harford, Jarrad, and Aditya Kaul, 2005, Correlated Order Flow: Persvasiveness, Sources and Pricing Effects, Journal of Financial and Quantitative Analysis 40, 29-55.
Hasbrouck, Joel, and Duane J. Seppi, 2001, Common factors in prices, order flows, and liquidity, Journal of Financial Economics 59, 383-411.
Ho, Thomas, and Hans H. Stoll, 1980, On dealer markets under competition, Journal of Finance 35, 259-267.
Huberman, Gur, and Dominika Halka, 2001, Systematic liquidity, Journal of Financial Research 24, 161-178.
Kamara, Avi, Xiaoxia Lou, and Ronnie Sadka, 2008, The divergence of liquidity commonality in the cross-section of stocks, Journal of Financial Economics 89, 444-466.
Kaniel, Ron, Gideon Saar, and Sheridan Titman, 2008, Individual investor trading and stock returns, Journal of Finance 63, 273-310.
Karolyi, G. Andrew, Kuan-Hui Lee, and Mathijs A. Van Dijk, 2008, Commonality in returns, liquidity and trading volume around the world, Working paper, Ohio State University.
Kiyotaki, Nobuhiro, and John Moore, 1997, Credit cycles, Journal of Political Economy, 105, 211-248.
Krishnamurthy, Arvind, 2002, The bond/old bond spread, Journal of Financial Economics 66, 463-506.
Kyle, Pete, and Wei Xiong, 2001, Contagion as a wealth effect, Journal of Finance 4, 1401-1440.
Lee, Charles M.C, 1992, Earnings news and small traders: An intraday analysis. Journal of Accounting and Economics 15, 265-302.
37
Lee, Charles M. C., and Balakrishna Radhakrishna, 2000, Inferring investor behavior: Evidence from TORQ data, Journal of Financial Markets 3, 83-111.
Lee, Charles M. C., and Mark J. Ready, 1991, Inferring trade direction from intraday data, Journal of Finance 46, 733-746.
Mitchell, Mark, Lasse Heje Pedersen, and Todd Pulvino, 2007, Slow moving capital, American Economic Review 97, 215-220.
Morck, Randall, Bernard Yeung, and Wayne Yu, 2000, The information content of stock markets: Why do emerging markets have synchronous stock price movements? Journal of Financial Economics 59, 215-260.
Morris, Stephen, and Hyun Song Shin, 2004, Liquidity black holes, Review of Finance 8, 1-18.
Naik, Narayan, and Pradeep Yadav, 2003, Risk management with derivatives by dealers and market quality in government bond markets, Journal of Finance 5, 1873-1904.
Roll, Richard, 1988, R2, Journal of Finance 42, 541-566.
Pastor, Lubos, and Robert F. Stambaugh, 2003, Liquidity risk and expected stock returns, Journal of Political Economy 111, 642-685.
Sadka, Ronnie, 2006, Momentum and post-earnings-announcement drift anomalies: The role of liquidity risk, Journal of Financial Economics 80, 309-349.
Shefrin, Hersh, and Meir Statman, 1985, The disposition to sell winners too early and ride losers too long: Theory and evidence, Journal of Finance 40, 777-790.
Stoll, Hans R., 1978, The supply of dealer services in securities markets, Journal of Finance 33, 1133-1152.
Vayanos, Dimitri, 2004, Flight to quality, flight to liquidity and the pricing of risk, NBER working paper.
Xiong, Wei, 2001, Convergence trading with wealth effects: An amplification mechanism in financial markets, Journal of Financial Economics 62, 247-292.
38
Table I Descriptive Statistics: Raw and Adjusted Spreads
This table presents the summary statistics of the annual average of the daily proportional quoted spread (QSPR) and adjusted spread (ASPR) for the sample period January 1988 to December 2003. For each firm i on day s, QSPRi,s is the average spread of all transactions within a day. The daily quoted spreads are adjusted for seasonality to obtain the adjusted spreads, ASPRi,s:
,2121 ,,5,4,3,2
,1
11
1,,
4
1,,,
sisisisisi
sik
skkik
skkisi
ASPRYEARfYEARfTICKfTICKf
HOLIDAYfMONTHeDAYdQSPR
+++++
++= ∑∑==
where we employ (i) day of the week dummies (DAYk,s) for Monday through Thursday ; (ii) month dummies (MONTHk,s) for January through November; (iii) a dummy for the trading days around holidays (HOLIDAYs); (iv) tick change dummies (TICK1s, TICK2s) to capture the tick change from 1/8 to 1/16 on 06/24/1997 and the change from 1/16 to the decimal system on 01/29/2001, respectively; (v) and time trend variables YEAR1s (YEAR2s), equal to the difference between the current calendar year and the year 1988 (1997) or the first year when the stock is traded on NYSE, whichever is later.
Year Number
QSPR (Unadjusted Proportional Quoted Spread)
ASPR (Adjusted Proportional Quoted Spread)
of Securities Mean Median
Coefficient of
Variation Mean Median
Coefficient of
Variation
1988 1027 1.26% 1.04% 0.618 1.33% 1.08% 0.641 1989 1083 1.13% 0.91% 0.671 1.24% 0.98% 0.708 1990 1146 1.41% 1.09% 0.720 1.56% 1.23% 0.748 1991 1224 1.32% 1.02% 0.712 1.50% 1.16% 0.723 1992 1320 1.25% 0.98% 0.714 1.47% 1.17% 0.703 1993 1430 1.18% 0.92% 0.736 1.45% 1.17% 0.692 1994 1497 1.14% 0.90% 0.717 1.47% 1.20% 0.657 1995 1562 1.06% 0.82% 0.741 1.43% 1.17% 0.657 1996 1641 0.97% 0.74% 0.769 1.38% 1.15% 0.649 1997 1709 0.77% 0.59% 0.812 1.31% 1.07% 0.670 1998 1709 0.78% 0.57% 0.834 1.32% 1.07% 0.692 1999 1607 0.85% 0.62% 0.822 1.34% 1.11% 0.679 2000 1482 0.93% 0.62% 0.930 1.38% 1.15% 0.666 2001 1328 0.55% 0.32% 1.213 1.38% 1.15% 0.648 2002 1243 0.39% 0.21% 1.266 1.26% 1.06% 0.657 2003 1200 0.26% 0.13% 1.251 1.13% 0.95% 0.692
39
Table II Spreads and Returns
Weekly changes in adjusted spreads for each security (ΔASPRi,t) are regressed on lagged market and idiosyncratic stock returns.
Panel A uses the regression specification: tik ktikik ktmkiiti RRASPR ,4
1 ,,4
1 ,,, variables control εγβα ++++=Δ ∑∑ = −= − ,
where ASPRi,t is stock i’s seasonally adjusted proportional spread in week t; Rm,t is the week t return on the CRSP value-weighted index; and Ri,t is the idiosyncratic return on stock i in week t. The firm-specific weekly control variables are: turnover (TURNi,t); relative order imbalance (ROIBi,t,); and idiosyncratic volatility (STDi,t). We also include the volatility of the market return in week t (STDm,t). The Δ operator represents the first-order difference operator. In Panel B, we add an interaction dummy variable DDOWN,m,t (DDOWN,i,t), which take the value of one if and only if Rm,t (Ri,t) is less than zero, that is,
, variables control ,4
1 ,,,,,4
1 ,,4
1 ,,,,,4
1 ,,, tik ktiDOWNktikiDOWNk ktikik ktmDOWNktmkiDOWNk ktmkiiti DRRDRRASPR εγγββα ++++++=Δ ∑∑∑∑ = −−= −= −−= −
Panel C uses the specification:
,variablescontrol ,4
1 ,,,,,4
1 ,,,,,
4
1 ,,4
1 ,,,,,4
1 ,,,,,4
1 ,,,
tik ktiLARGEUPktikiLARGEUPk ktiLARGEDOWNktikiLARGEDOWN
k ktikik ktmLARGEUPktmkiLARGEUPk ktmLARGEDOWNktmkiLARGEDOWNk ktmkiiti
DRDR
RDRDRRASPR
εγγ
γβββα
++++
++++=Δ
∑∑∑∑∑∑
= −−= −−
= −= −−= −−= −
where DDOWN LARGE,m,t (DUP LARGE,m,t ) is a dummy variable that is equal to one if and only if Rm,t is more than 1.5 standard deviations below (above) its unconditional mean. Cross-sectional means (t-statistics), medians, and percentage of significant coefficient estimates at the 5% level (one-tailed) are reported below.
Panel A: Spreads and Lagged Returns
Estimated Coefficients R m,t-1 R m,t-2 R m,t-3 R m,t-4 R i,t-1 R i,t-2 R i,t-3 R i,t-4 Mean -0.830 -0.397 -0.216 -0.052 -0.549 -0.282 -0.177 -0.089 (t-statistics) (-17.19) (-8.15) (-4.48) (-1.09) (-27.26) (-13.92) (-8.73) (-4.43) Median -0.528 -0.234 -0.101 -0.003 -0.423 -0.200 -0.117 -0.051 % positive (negative) (98.4%) (86.8%) (71.6%) (50.5%) (98.9%) (94.1%) (86.2%) (72.2%)
% positive (negative) significant (78.2%) (35.4%) (13.9%) (6.0%) (92.7%) (63.5%) (38.0%) (15.9%)
Estimated Coefficients ΔSTD m,t-1 ΔSTD i,t-1 ΔTurn i,t-1 ΔOIB i,t-1 ΔSTD m, t ΔSTD i, t Mean 0.221 0.233 -0.019 0.008 0.311 0.213 (t-statistics) (1.71) (5.90) (-4.01) (0.68) (4.35) (8.78) Median 0.147 0.162 -0.010 0.006 0.159 0.169 % positive (negative) 63.2% 78.5% (76.7%) 54.7% 73.3% 85.0%
% positive (negative) significant 11.4% 27.6% (20.7%) 9.4% 20.4% 45.8%
40
Panel B: Spreads and Signed Lagged Returns Estimated Coefficients R m,t-1 R m,t-2 R m,t-3 R m,t-4 R i,t-1 R i,t-2 R i,t-3 R i,t-4
Mean -0.413 -0.321 -0.307 -0.163 -0.473 -0.298 -0.204 -0.126 (t-statistics) (-4.10) (-3.55) (-3.47) (-1.89) (-12.61) (-9.20) (-6.34) (-3.93) Median -0.221 -0.195 -0.175 -0.051 -0.334 -0.209 -0.134 -0.073 % positive (negative) (73.9%) (73.3%) (71.4%) (58.0%) (91.3%) (89.4%) (80.4%) (69.9%) % positive (negative) significant (15.4%) (14.5%) (12.1%) (6.7%) (56.5%) (42.2%) (24.8%) (14.9%)
Estimated Coefficients R m,t-1 × DDown,m,t-1
R m,t-2 × DDown,m,t-2
R m,t-3 × DDown,m,t-3
R m,t-4 × DDown,m,t-4
R i,t-1 × DDown,i,t-1
R i,t-2 × DDown,i,t-2
R i,t-3 × DDown,i,t-3
R i,t-4 × DDown,i,t-4
Mean -0.810 -0.038 0.257 0.208 -0.158 0.048 0.073 0.094 (t-statistics) (-4.79) (-0.25) (1.83) (1.42) (-2.33) (0.83) (1.28) (1.65) Median -0.443 0.028 0.155 0.086 -0.117 0.036 0.040 0.057 % positive (negative) (76.7%) (48.0%) 62.3% 57.9% (63.1%) 56.3% 56.5% 59.1% % positive (negative) significant (17.2%) (4.6%) 8.9% 6.0% (15.1%) 7.9% 7.9% 9.1%
Panel C: Spreads and the Magnitude of Lagged Market Returns
Estimated Coefficients R m,t-1 R m,t-2 R m,t-3 R m,t-4 R m,t-1 × DDownLarge,m,t-1
R m,t-2 × DDownLarge,m,t-2
R m,t-3 × DDownLarge,m,t-3
R m,t-4 × DDownLarge,m,t-4
Mean -0.715 -0.308 -0.203 -0.153 -0.430 -0.063 0.121 0.234 (t-statistics) (-10.00) (-4.30) (-2.84) (-2.15) (-3.56) (-0.55) (1.03) (2.01) Median -0.459 -0.192 -0.097 -0.042 -0.196 0.024 0.088 0.094 % positive (negative) (92.2%) (74.4%) (64.6%) (57.1%) (68.1%) (47.0%) 58.6% 60.1% % positive (negative) significant (46.6%) (19.9%) (10.3%) (8.2%) (13.4%) (5.1%) 7.0% 7.9%
Estimated Coefficients R m,t-1 × DUpLarge,m,t-1
R m,t-2 × DUpLarge,m,t-2
R m,t-3 × DUpLarge,m,t-3
R m,t-4 × DUpLarge,m,t-4
Mean 0.161 -0.222 -0.209 0.065 (t-statistics) (1.30) (-1.55) (-1.51) (0.54) Median 0.113 -0.066 -0.094 0.001 % positive (negative) 60.8% (57.6%) (59.3%) 50.2% % positive (negative) significant 6.6% (7.1%) (7.6%) 5.4%
41
Table III Spreads, Market Returns, and Impact of the Funding Market Proxies
Weekly changes in the adjusted spreads for each security (ΔASPRi,t) are regressed on signed lagged market returns with an interaction dummy variable DCAP,t that is equal to one when the funding market is likely to face capital constraints in week t:
titCAPtmDOWNtmiCAPDOWNk ktmDOWNktmkiDOWNk ktmkiiti DDRDRRASPR ,1,1,,1,1,,,4
1 ,,,,,4
1 ,,, variablescontrol εβββα +++++=Δ −−−= −−= − ∑∑ .
All other variables are defined in Table II. In Panel A, DCAP,t is equal to one when the excess return on a portfolio of investment banks in week t is negative. DCAP,t in Panel B is equal to one when there is a decrease in the aggregate repos in week t. Finally, when there is an increase in the commercial paper spread, we assign a value of one to DCAP,t in Panel C.
Panel A: Investment Bank & Broker Sector Returns
Estimated Coefficients R m,t-1 R m,t-2 R m,t-3~t-4 R m,t-1 ×
DDown,m,t-1 R m,t-2 ×
DDown,m,t-2 R m,t-3~t-4 ×
DDown,m,t-3~t-4 R m,t-1 × DDown,m,t-1
× DCAP,t-1 Mean -0.413 -0.333 -0.230 -0.673 -0.026 0.216 -0.297 (t-statistics) (-4.13) (-3.72) (-3.69) (-3.82) (-0.18) (1.97) (-2.20) Median -0.210 -0.196 -0.118 -0.353 0.035 0.136 -0.155 % positive (negative) (74.0%) (73.9%) (71.1%) (72.7%) (46.9%) 65.8% (61.8%) % positive (negative) significant (14.4%) (15.6%) (11.7%) (14.7%) (4.4%) 9.0% (10.6%)
Panel B: Change in Repos
Estimated Coefficients R m,t-1 R m,t-2 R m,t-3~t-4 R m,t-1 ×
DDown,m,t-1 R m,t-2 ×
DDown,m,t-2 R m,t-3~t-4 ×
DDown,m,t-3~t-4 R m,t-1 × DDown,m,t-1
× DCAP,t-1
Mean -0.426 -0.334 -0.210 -0.528 -0.044 0.207 -0.672 (t-statistics) (-4.37) (-3.83) (-3.45) (-3.06) (-0.30) (1.93) (-4.98) Median -0.230 -0.197 -0.110 -0.264 0.030 0.139 -0.372 % positive (negative) (75.4%) (74.0%) (69.2%) (68.3%) (47.9%) 65.8% (75.4%) % positive (negative) significant (15.6%) (15.4%) (10.6%) (10.7%) (4.7%) 9.0% (20.3%)
Panel C: Commercial Paper Spread
Estimated Coefficients R m,t-1 R m,t-2 R m,t-3~t-4 R m,t-1 ×
DDown,m,t-1 R m,t-2 ×
DDown,m,t-2 R m,t-3~t-4 ×
DDown,m,t-3~t-4 R m,t-1 × DDown,m,t-1
× DCAP,t-1
Mean -0.433 -0.320 -0.218 -0.492 -0.042 0.202 -0.453 (t-statistics) (-4.36) (-3.59) (-3.53) (-2.57) (-0.28) (1.85) (-3.34) Median -0.230 -0.187 -0.114 -0.248 0.015 0.132 -0.267 %positive(negative) (75.0%) (72.8%) (70.0%) (65.3%) (48.8%) 65.4% (71.9%)
%positive(negative) significant (15.6%) (14.5%) (11.1%) (8.6%) (4.6%) 8.9% (14.1%)
42
Table IV Spreads and Returns: Cross-sectional Estimates
Stocks are sorted into nine size-volatility portfolios using two-way dependent sorts on market capitalization and return volatility. Weekly changes in portfolio average adjusted spreads (ΔASPRp,t) are regressed on lagged market returns (Rm,t) and portfolio-specific returns (Rp,t) using the SUR method:
,variablescontrol ,4
1 ,,,,,4
1 ,,4
1 ,,,,,4
1 ,,, tpk ktpDOWNktpkpDOWNk ktpkpk ktmDOWNktmkpDOWNk ktmkpitp DRRDRRASPR εγγββα ++++++=Δ ∑∑∑∑ = −−= −= −−= −
where DDOWN,m,t (DDOWN,p,t) is a dummy variable that is one if and only if Rm,t (Rp,t) is less than zero. The control variables are defined in Table II. t-statistics are reported in parentheses. The “High-Low” column, reports the test of the null hypothesis that the coefficients corresponding to the High and Low Volatility portfolios are equal, and significant differences at the 99%, 95%, and 90% confidence levels are indicated by ***, **, and *, respectively. Small-Size Medium-Size Large-Size
High Volatility
Medium Volatility
Low Volatility
High - Low
High Volatility
Medium Volatility
Low Volatility
High - Low
High Volatility
Medium Volatility
Low Volatility
High - Low
Rm,t-1 -1.23 -0.47 -0.38 -0.85*** -0.27 -0.21 -0.24 -0.04 -0.13 -0.10 -0.08 -0.05 (-4.34) (-2.69) (-3.04) (-2.76) (-2.50) (-3.59) (-2.33) (-2.26) (-2.25) Rm,t-2 -0.57 -0.61 -0.25 -0.31 -0.24 -0.21 -0.18 -0.06 -0.13 -0.10 -0.10 -0.03 (-2.14) (-3.81) (-2.22) (-2.68) (-2.78) (-2.95) (-2.58) (-2.27) (-2.88) Rm,t-3~t-4 -0.39 -0.37 -0.33 -0.06 -0.16 -0.15 -0.08 -0.08 -0.05 -0.02 -0.02 -0.03 (-2.13) (-3.30) (-4.06) (-2.45) (-2.81) (-1.88) (-1.25) (-0.80) (-0.69) Rm,t-1×DDown,m,t-1 -1.74 -1.26 -0.71 -1.03*** -0.67 -0.57 -0.40 -0.28*** -0.34 -0.29 -0.21 -0.13** (-3.85) (-4.40) (-3.44) (-4.11) (-4.10) (-3.57) (-3.65) (-3.75) (-3.43) Rm,t-2×DDown,m,t-2 0.24 0.32 0.03 0.21 0.10 0.09 0.07 0.03 0.12 0.10 0.15 -0.03 (0.58) (1.24) (0.14) (0.67) (0.75) (0.66) (1.45) (1.43) (2.62) Rm,t-3~t-4×DDown,m,t-3~t-4 0.63 0.51 0.50 0.13 0.28 0.27 0.14 0.14 0.14 0.09 0.08 0.06 (2.17) (2.71) (3.67) (2.53) (2.89) (1.86) (2.20) (1.77) (1.84)
Rp,t-1 -1.92 -0.98 -0.61 -1.30*** -0.55 -0.43 -0.39 -0.16* -0.25 -0.19 -0.16 -0.10* (-8.17) (-6.19) (-4.84) (-5.24) (-4.63) (-5.01) (-4.53) (-4.40) (-3.33) Rp,t-2 -0.28 -0.13 -0.22 -0.06 -0.11 -0.13 -0.19 0.08 -0.15 -0.13 -0.02 -0.12 (-1.23) (-0.87) (-1.82) (-1.07) (-1.45) (-2.54) (-2.76) (-3.19) (-0.53)
Rp,t-3~t-4 -0.24 -0.18 -0.05 -0.19 -0.03 -0.03 -0.06 0.03 -0.01 -0.03 -0.05 0.04 (-1.63) (-1.79) (-0.54) (-0.46) (-0.54) (-1.06) (-0.31) (-1.00) (-1.65) Rp,t-1×DDown,p,t-1 0.78 0.37 -0.03 0.80** 0.07 0.03 0.02 0.05 -0.08 -0.10 -0.08 0.00 (1.87) (1.40) (-0.12) (0.40) (0.21) (0.15) (-0.82) (-1.31) (-0.90) Rp,t-2×DDown,p,t-2 -0.06 -0.35 -0.07 0.01 -0.24 -0.20 -0.03 -0.21 0.18 0.18 0.01 0.18 (-0.15) (-1.38) (-0.31) (-1.38) (-1.28) (-0.24) (1.96) (2.48) (0.09) Rp,t-3~t-4×Down,p,t-3~t-4 0.18 -0.02 -0.22 0.39 -0.13 -0.10 -0.01 -0.11 -0.06 -0.03 0.09 -0.15 (0.66) (-0.08) (-1.46) (-1.01) (-0.95) (-0.15) (-0.86) (-0.62) (1.49)
43
Table V Liquidity Betas and Market Returns
Weekly changes in adjusted spreads for each security (ΔASPRi,t) are regressed on lagged market returns (Rm,t), idiosyncratic stock returns (Ri,t), and the change in market average spreads (ΔASPRm,t ) using the following two specifications:
tik ktiDOWNktikiDOWNk ktikik ktmDOWNktmkiDOWN
k ktmkitmDOWNtmiDOWNLIQtmiLIQiti
DRRDRRDASPRbASPRbASPR
,4
1 ,,,,,4
1 ,,4
1 ,,,,,
4
1 ,,,,,,,,,,
variablescontrol εγγββα
++++++Δ+Δ+=Δ
∑∑∑∑
= −−= −= −−
= −
,variablescontrol ,
4
1 ,,,,,4
1 ,,4
1 ,,,,,
4
1 ,,,,,,,,,,,,,,,
tik ktiDOWNktikiDOWNk ktikik ktmDOWNktmkiDOWN
k ktmkitmLARGEDOWNtmiLARGEDOWNLIQtmSMALLDOWNtmiSMALLDOWNLIQtmiLIQiti
DRRDR
RDASPRbDASPRbASPRbASPR
εγγβ
βα
++++
++Δ+Δ+Δ+=Δ
∑∑∑∑
= −−= −= −−
= −
where DDOWN,m,t is a dummy variable that is equal to one if and only if Rm,t (Ri,t) is less than zero, DDOWN SMALL,m,t is a dummy variable that is equal to one if and only if Rm,t is negative and less than 1.5 standard deviations below its unconditional mean return, DDOWN LARGE,m,t is a dummy variable that is equal to one if and only if Rm,t is more than 1.5 standard deviations below its unconditional mean. All other variables are defined in Table II.
Panel A
Estimated Coefficients R m,t-1 R m,t-2 R m,t-3~t-4
R m,t-1 × DDown,m,t-1
R m,t-2 × DDown,m,t-2
R m,t-3~t-4 × DDown,m,t-3~t-4
ΔASPR m,t ΔASPR m,t ×
DDown,m,t
Mean -0.419 -0.227 -0.161 -0.293 -0.281 0.091 0.562 0.310 (t-statistics) (-21.62) (-12.50) (-12.36) (-9.83) (-9.90) (4.32) (46.34) (19.76) Median -0.211 -0.125 -0.074 -0.125 -0.136 0.061 0.381 0.208 %positive(negative) (74.7%) (65.3%) (63.0%) (58.7%) (60.9%) 56.8% 91.5% 73.7%
%positive(negative) significant
(15.5%) (10.0%) (8.5%) (7.0%) (8.2%) 5.6% 57.0% 27.8%
Panel B
Estimated Coefficients R m,t-1 R m,t-2 R m,t-3~t-4
R m,t-1 × DDown,m,t-1
R m,t-2 × DDown,m,t-2
R m,t-3~t-4 × DDown,m,t-3~t-4
ΔASPR m,t ΔASPR m,t × DDownSmall,m,t
ΔASPR m,t × DDownLarge,m,t
Mean -0.424 -0.227 -0.163 -0.294 -0.277 0.097 0.561 0.268 0.387 (t-statistics) (-19.33) (-11.14) (-11.33) (-8.48) (-8.59) (4.06) (43.09) (13.13) (23.07) Median -0.212 -0.125 -0.077 -0.124 -0.140 0.067 0.381 0.173 0.252 %positive(negative) (74.5%) (65.8%) (63.6%) (59.0%) (60.5%) 57.7% 91.5% 67.0% 73.0%
%positive(negative) significant
(15.7%) (10.0%) (8.7%) (6.8%) (8.0%) 6.3% 57.0% 22.4% 27.3%
44
Table VI Commonality in Liquidity and Market Returns
Daily changes in adjusted spread for each stock are regressed on changes in market average spreads within each month t to generate monthly R2 values. Commonality in liquidity in month t (LIQCOMt) is defined as the logit transformation of the cross-section average R2. Commonality in order imbalance in month t (ROIBCOMt) is obtained from within-month regressions of daily individual firm relative order imbalance on the market average, similar to LIQCOMt. We estimate the following regression equations:
ttLARGEUPtmLARGEUPtLARGEDOWNtmLARGEDOWNtmt controlsDRDRRaLIQCOM εβββ +++++= ,,,,,
,,,,,, ttLARGEUPtmLARGEUPtLARGEDOWNtmLARGEDOWNtmt controlsDRDRRaROIBCOM εβββ +++++=
where the dummy variable DDownLarge,m,t (DUpLarge,m,t ) is equal to one if the market return in month t (Rm,t) is more than 1.5 standard deviations below (above) its unconditional mean. The control variables include ROIB, the cross-sectional average relative order imbalance level; equity mutual fund flows as a proportion of total mutual fund investment; and market volatility (STDm). The first four columns present OLS estimates while the last two columns present estimates from a two-stage least squares (2SLS) regression. t-statistics are reported in parentheses.
OLS 2SLS Dependent Variables
Liquidity Commonality
ROIB Commonality
Liquidity Commonality
ROIB Commonality
Intercept -2.102 -2.005 -0.647 -2.432 -0.649 (-9.91) (-7.19) (-2.70) (-7.47) (-1.07)
R m,t 0.233 -0.040 -1.650 -0.409 -1.650 (0.35) (-0.06) (-4.32) (-0.62) (-4.11)
R m,t * -3.715 -2.392 1.919 -2.116 1.916 DDownLarge,m,t (-3.06) (-1.80) (2.61) (-1.87) (2.11)
R m,t * -0.696 -1.247 0.632 -1.180 0.631 DUpLarge,m,t (-0.97) (-1.65) (0.85) (-1.08) (0.88)
STDm,t 0.115 0.079 0.135 0.079 (2.40) (2.71) (2.86) (2.09)
ROIBt 1.316 1.730 (1.78) (2.61)
ROIB 0.182 0.082 -0.119 Commonality t (2.14) (0.90) (-0.88)
Liquidity 0.096 0.095 Commonality t (1.81) (0.41)
ROIB 0.499 0.499 Commonalityt-1 (7.91) (7.50)
Mutual Fund -0.652 -0.653 Flow t (-2.88) (-2.42)
45
Table VII Commonality in Liquidity, Market Returns, and Industry Returns
Daily changes in adjusted spreads for each stock are regressed on changes in industry average spreads within each month to generate monthly R2 values and liquidity betas (bLIQ,t). Commonality in liquidity (LIQCOMt) is defined as the logit transformation of the cross-section average R2 for all stocks within the same industry in each month. We estimate the following regressions:
ttMKTjDOWNtMKTjDOWNtMKTj
tINDjDOWNtINDjDOWNtINDjtINDj
DRR
DRRaLIQCOM
εββ
δδ
+++
++=
,,,,
,,,,,
,,,,,,,,
,,,,,,,,
ttMKTjLARGEUPtMKTjLARGEUPtMKTjLARGEDOWNtMKTjLARGEDOWNtMKTj
tINDjLARGEUPtINDjLARGEUPtINDjLARGEDOWNtINDjLARGEDOWNtINDjtINDj
DRDRR
DRDRRaLIQCOM
εβββ
δδδ
++++
+++=
where RINDj,t and RMKTj,t denote the month t return on the value-weighted returns on industry j and the market (excluding industry j). The dummy variable DDown,INDj,t (DDownLarge,INDj,t) is equal to one if RINDj,t is less than zero (more than 1.5 standard deviations below its mean). DDown,MKTj,t (DDownLarge,MKTj,t) is similarly defined based on RMKTj,t. In the last two columns, we replace LIQCOMt with liquidity betas (bLIQ,t) as the dependent variable. White’s heteroskedasticity- consistent t-statistics are reported in parentheses.
Dependent Variable LIQCOM Liquidity Betas
-2.438 -2.405 0.668 0.711 Intercept (-271.1) (-401.05) (60.41) (97.69)
R INDj,t 0.192 -0.023 0.159 -0.178 (1.15) (-0.15) (0.72) (-0.88)
R MKTJ,t 0.327 -0.206 1.074 0.327 (1.35) (-1.02) (3.46) (1.29)
R INDj,t * -0.986 -0.999 DDown,INDj,t (-3.01) (-2.69)
R MKTj,t * -1.995 -2.122 DDown,MKTj,t (-4.39) (-4.06)
R INDj,t * -0.875 -0.701 DDownLarge,INDj,t (-3.10) (-2.25)
R INDj,t * 0.098 0.292 DUpLarge,IND,t (0.48) (1.01)
R MKTj,t * -1.359 -0.726 DDownLarge,MKTj,t (-3.86) (-1.77)
R MKTj,t * 0.210 -0.039 DUpLarge,MKTj,t (0.72) (-0.10)
46
Table VIII Contrarian Profits and Market Returns
Weekly stock returns are sorted into winner (loser) portfolios if the returns are above (below) the median of all positive (negative) returns in week t. Contrarian portfolio weight for stock i in week t is given by: ,/)(
1 1,1,1,1,,, ∑= −−−−=Np
i tititititip TurnRTurnRw
where Ri,t and Turni,t are stock i’s return and turnover in week t. Contrarian profits for week t+k, for k=1,2,3, and 4 are reported in Panel A. Panel B reports contrarian profits conditional on market returns. Large Up (Large Down) refers to cumulative market returns from week t-4 to t-1 being more than 1.5 standard deviations above (below) the mean. Small Up (Small Down) market refers to cumulative market returns between zero and 1.5 (-1.5) standard deviations. Factor-adjusted returns represent the alphas from regressing the returns on the Fama-French three factors: market, size, and book-to-market. Newey-West autocorrelation-corrected t-statistics are given in parentheses.
Panel A: Unconditional Contrarian Profits Week
Portfolio t+1 t+2 t+3 t+4 Loser 0.75% 0.43% 0.39% 0.37% Winner 0.17% 0.29% 0.37% 0.41% Loser minus Winner 0.58% 0.14% 0.03% -0.04% (t-statistics) (5.38) (1.69) (0.38) (-0.52)
Panel B: Contrarian Profits Conditional on Market Returns Week t+1
Past Market Return Portfolio Large Up Small Up Small Down Large Down
Loser 0.54% 0.83% 0.48% 1.37%
Winner -0.10% 0.29% -0.04% 0.19%
Loser minus Winner 0.64% 0.54% 0.52% 1.18% (t-statistics) (0.93) (4.07) (2.51) (3.01)
Loser minus Winner (adjusted for French-French factors) 0.57% 0.48% 0.50% 1.16%
(t-statistics) (0.83) (3.83) (2.41) (2.90)
Week t+2 Past Market Return Portfolio
Large Up Small Up Small Down Large DownLoser 0.86% 0.44% 0.21% 0.97%
Winner 0.43% 0.40% 0.09% 0.07%
Loser minus Winner 0.43% 0.03% 0.12% 0.90% (t-statistics) (1.21) (0.33) (0.88) (1.93)
Loser minus Winner (adjusted for Fama-French factors) 0.34% -0.01% 0.12% 0.84%
(t-statistics) (0.88) (-0.09) (0.87) (1.88)
47
Table IX Limit Order Trading Profits
At the beginning of each week, a stock is sorted into sell (buy) portfolio if its price hits x% above (below) its opening price. If the stock price hits the limit, the stock is added to the buy or sell portfolios, with the stock’s weight proportional to its turnover (Turni,t) in the ranking week, i.e., the weight for firm i in week t is Turni,t / ∑ = −
Np
i tiTurn1 1,
.
We consider x equal to 3%, 5%, or 7%. Contrarian profits in weeks t+1 and t+2 are reported in Panel A. Panel B reports contrarian profits conditional on lagged market returns. Large Up (Large Down) refers to cumulative market returns from week t-4 to t-1 being more than 1.5 standard deviations above (below) the mean return. Small Up (Small Down) market refers to cumulative market returns between zero and 1.5 (-1.5) standard deviations. Newey-West autocorrelation-corrected t-statistics are given in parentheses.
Panel A: The Unconditional Profits of Limit Order Contrarian Strategy Open Price +/- 3% Open Price +/- 5% Open Price +/- 7%
Week Week Week Portfolio
t+1 t+2 t+1 t+2 t+1 t+2 Limit Buy 0.70% 0.40% 0.93% 0.39% 1.07% 0.39% Limit Sell 0.33% 0.30% 0.21% 0.29% 0.10% 0.29%
Buy-minus-Sell 0.37% 0.10% 0.71% 0.10% 0.97% 0.09% (t-statistics) (7.69) (2.59) (10.47) (1.64) (9.65) (1.02)
Panel B: Profits of Limit Order Contrarian Strategy
Conditional on Market Returns in week t+1 Criteria = Open Price +/- 3%
Past Market Return Portfolio Large Up Small Up Small Down Large Down
Limit Buy 0.58% 0.72% 0.62% 0.90% Limit Sell 0.24% 0.41% 0.29% -0.06%
Buy-minus-Sell 0.33% 0.31% 0.34% 0.96% (t-statistics) (1.51) (5.70) (4.05) (4.16) Criteria = Open Price +/- 5%
Past Market Return Portfolio
Large Up Small Up Small Down Large Down Limit Buy 0.68% 0.96% 0.79% 1.36% Limit Sell 0.04% 0.33% 0.12% -0.21%
Buy-minus-Sell 0.64% 0.63% 0.68% 1.56% (t-statistics) (1.81) (7.52) (5.52) (5.17) Criteria = Open Price +/- 7%
Past Market Return Portfolio Large Up Small Up Small Down Large Down
Limit Buy 0.76% 1.12% 0.86% 1.73% Limit Sell -0.10% 0.24% -0.01% -0.40%
Buy-minus-Sell 0.86% 0.88% 0.87% 2.13% (t-statistics) (1.75) (6.72) (5.36) (4.89)
48
Figure 1. A time-series plot of the average raw and adjusted quoted spreads. The figure below shows the cross-sectional mean of the raw and adjusted proportional quoted spreads for a constant sample of stocks that have valid observations throughout the full sample period: 1988-2003.
Figure 2. The time-series variation in liquidity commonality.
Jan-88 Jan-89 Jan-90 Jan-91 Jan-92 Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Dec-03
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2q y
Time
← Gulf War I
← Asia Financial Crisis
← LTCM Crisis
← September 11 Crisis
← Worldcom Scandal
49
1 This spiral effect of a drop in collateral value is emphasized in a number of theoretical papers, starting with the foundational work in Kiyotaki and Moore (1997), where lending is based on the value of land as collateral. See also Allen and Gale (2005). 2 Adrian and Shin (2008) show that the changes in the balance sheets of financial intermediaries are linked to funding liquidity through shifts in the market wide risk appetite. In Eisfeldt (2004), liquidity is endogenously determined and procyclical: assets are less liquid in bad times. 3 Other related work includes Pastor and Stambaugh (2003), who show that liquidity is a priced state variable, and Amihud and Mendelson (1986), who show that illiquid assets earn higher returns. In Acharya and Pedersen (2005), a fall in aggregate liquidity primarily affects illiquid assets. Sadka (2006) documents that the earnings momentum effect is partly due to higher liquidity risk. 4 Karolyi, Lee, and Dijk (2008) report a similar asymmetric effect of market returns on liquidity commonality in other developed as well as developing equity markets. 5 A sharp short-term price reversal due to liquidity shocks is predicted by models such as Campbell, Grossman and Wang (1993) and Morris and Shin (2004). Pastor and Stambaugh (2003) use a similar idea to show that liquidity risk is priced and liquidity events seem to occur often after large price declines (e.g., the crash of 1987). 6 The Internet Appendix to this text is available at http://www.afajof.org/supplements.asp . 7 Estimates of the regression equations based on spread levels (ASPRi,t ) instead of changes in spreads (ΔASPRi,t) produce qualitatively similar results at both monthly and weekly horizons. However, using changes in the variables has the advantage of reducing the econometric bias arising from highly autoregressive dependent and independent variables. Focusing our analysis at weekly intervals provides us a large number of time-series observations while minimizing measurement problems associated with daily returns. 8 We also consider the effect of up to eight weeks of lagged returns. These additional lags are in general insignificant and do not change our findings. The results are reported in the Internet Appendix. 9 Our results are unchanged when idiosyncratic returns are computed as the excess returns from a market model specification: (Rit – bi Rmt). 10 The t-statistics associated with the mean coefficients in Table II have been adjusted for cross-equation correlations. We extend the correction in standard errors proposed in Chordia, Roll, and Subrahmanyam (2000) by allowing the variance and pairwise covariances between coefficient estimates to vary across securities. The variance of each estimated coefficient βi is obtained from stock i’s liquidity-return regression in equation (2). The empirical correlation between the regression residuals for stocks i and j is used to estimate the pairwise correlation between the coefficients βi and βj. Hence, the standard error of the mean estimated coefficient is provided by:
∑ ∑∑∑= ≠===
+==N
i
N
ijjjiji
N
ii
N
ii VarVarVar
NNStdDevStdDev
1 ,1,
11)()()(1)1()( ββρβββ .
11 To alleviate any concerns arising from the fact that the firm-specific control variables in equation (2) are correlated with spreads, we re-estimate the equation without these controls. We continue to find that changes in spreads are (more) sensitive to (negative) market returns.
50
12 We also consider other cut-offs of 2.0 and 1.0 standard deviations from the mean to identify large market return states and obtain similar results. 13 Recent behavioral models argue that a positive relation between past returns and firm liquidity could arise from an increase in the supply of overconfident individual traders following price run-ups (Gervais and Odean (2001)), overreaction to sentiment shocks ((Baker and Stein (2004)), or disposition effects (Shefrin and Statman (1985)). We examine this possibility using the percentage of small trades, defined as trades below $5000, to proxy for uninformed, behaviorally biased trades by individuals (see Lee (1992), Lee and Radhakrishna (2000), Barber, Odean and Zhu (2008)). While we find an increase in the percentage of small trades following positive market returns, we do not find any evidence of decreases in small trades following negative market returns. Hence, the asymmetric effect of market returns on liquidity cannot be explained by these behavioral biases. Detailed results are available in the Internet Appendix. 14 For example, in 1996, the 10 largest firms that belong to SIC code 6211 (Security Brokers, Dealers and Floatation Companies) are: Alex Brown, Bear Sterns, Dean Witter, A.G. Edwards, Lehmann Brothers, Merrill Lynch, Morgan Stanley, John Nuveen, Charles Schwab, and Travellers Group. The composition of firms is updated annually. Adrian and Shin (2008) use a similar portfolio of firms to examine the effect of changes in asset values on leverage of financial intermediaries. 15 We also consider additional lags to DCAP,t, but find them to be insignificant. The results are reported in the Internet Appendix. 16 Adrian and Shin (2008) argue that there is also a potential feedback effect: weaker balance sheets lead to greater sale of assets, which puts downward pressure on asset prices and leads to even weaker balance sheets. 17 We thank Tobias Adrian for generously sharing the weekly data on the primary dealer repo positions compiled by the Federal Reserve Bank of New York. 18 The weekly data are downloaded from the Federal Reserve website at www.federalreserve.gov. 19 For ease of exposition, we report the coefficients for the combined market (and portfolio) returns in weeks t-3 and t-4. 20 The industry classifications are obtained from Kenneth French’s website at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html 21 Pastor and Stambaugh (2003) use a similar motivation to develop a liquidity risk factor for empirical asset pricing models. 22 We thank Joel Hasbrouck for suggesting this alternative trading strategy. 23 The weekly returns on the three Fama-French factors are constructed using daily portfolio returns downloaded from Kenneth French’s data library.
1
Internet Appendix to “Stock Market Declines and Liquidity” *
Appendix A: Dynamic Conditional Correlation of Spreads and Market Returns
In this appendix, we examine the relationship between market returns and the conditional correlations in stock liquidity, measured by the dynamic conditional correlation (DCC) method proposed by Engle (2002). The DCC model relies on the parsimonious univariate GARCH estimates of liquidity for each asset and has a computational advantage over the multivariate GARCH model. The estimation starts with first obtaining a series of liquidity shocks from a univariate GARCH specification of the liquidity variable and. Then, in the second stage, we estimate the conditional correlation between asset liquidity shocks.
We use the DCC methodology to model the liquidity movements between a pair of portfolios. We consider pairs of size-sorted portfolios (small, medium, and large size portfolios) and also the correlation in liquidity between portfolios composed of S&P and non-S&P constituent stocks. We sort the stocks in our sample into three size portfolios (or S&P and non-S&P portfolios) and take the equally weighted average daily adjusted spread as the portfolio daily spread. As spreads tend to be highly autocorrelated, we fit an AR(1) model for average spreads and use the residuals as our liquidity variable. We obtain weekly dynamic correlation estimates between a pair of portfolio liquidity shocks by taking the average of all the daily DCC estimates in a week. Finally, we report the weekly dynamic correlations for each market state based on the magnitude and sign of market returns, as defined in the text in Section III.
Table IA.AI presents the conditional correlations in liquidity between size portfolios for each market state. The average DCC estimate of the correlation in spreads between large and small stock portfolios increases from 0.25 to 0.31 after a large negative market return. A large drop in market prices has a similar effect on conditional correlations between other pairs of size portfolios. The conditional correlation between liquidity of the S&P and non-S&P constituent stocks exhibits similar behavior: the conditional correlation between these two portfolio spreads increases after a large negative market return from 0.38 to 0.44. The DCC method confirms that the sharp increase in commonality in spreads following large market declines.
*Citation format: Allaudeen Hameed, Wenjin Kang, and S. Viswanathan, [year], Internet Appendix to “Stock Market Declines and Liquidity”, Journal of Finance [volume], [pages], http://www.afajof.org/[year].asp
2
Table IA.AI DCC Estimates Conditional on Market Returns
The sample stocks are sorted into three size portfolios (or the S&P and non-S&P constituent portfolios). The portfolio daily spread is the equally weighted average of the stock daily adjusted spread in the portfolio. We first obtain the portfolio spread residuals from a first-order autoregression model. The residuals for the corresponding pairs of portfolio spreads are then fitted using the DCC model with mean-reversion. The daily DCC estimates are averaged into the weekly dynamic correlation estimates. The weekly dynamic correlation conditional on market states is reported below. Market states are defined based on the cumulative CRSP value-weighted return from week t-4 to week t-1. Large Up (Large Down) refers to cumulative market returns being more than 1.5 standard deviations above (below) the mean. Small Up (Small Down) market refers to cumulative market returns between zero and 1.5 (-1.5) standard deviations. The DCC differences that are significant at the 99%, 95%, and 90% confidence level are labelled with ***, **, and *, respectively.
Past Market Return
DCC Estimates (a): Large
Up
(b): Small
Up
(c): Small Down
(d): Large Down
(e): Average excluding (d) (d) - (e)
DCC between small and large size portfolios 0.226 0.243 0.260 0.307 0.248 0.060***
DCC between small and medium size portfolios 0.394 0.399 0.405 0.451 0.401 0.051***
DCC between medium and large size portfolios 0.423 0.467 0.497 0.537 0.474 0.063***
DCC between S&P and non-S&P portfolios 0.362 0.372 0.393 0.442 0.378 0.063***
3
Appendix B: Supplementary Tables
Table IA.BI Proportional Effective Spreads and Returns
The empirical tests in this table are based on the proportional effective spread, which is two times the difference between the trade execution price and the midquote scaled by the midquote. Weekly changes in adjusted proportional effective spreads for each security are regressed on lagged market and idiosyncratic stock returns in Panel A, using the following regression specification:
tik ktiDOWNktikiDOWNk ktikik ktmDOWNktmkiDOWNk ktmkiiti DRRDRRASPR ,4
1 ,,,,,4
1 ,,4
1 ,,,,,4
1 ,,, variablescontrol εγγββα ++++++=Δ ∑∑∑∑ = −−= −= −−= −,
where ASPRi,t is stock i’s seasonally adjusted proportional effective spread in week t; Rm,t is the week t return on the CRSP value-weighted index; and Ri,t is the idiosyncratic return on stock i in week t. The firm-specific weekly control variables are: turnover (TURNi,t); relative order imbalance (ROIBi,t,); and idiosyncratic volatility (STDi,t). We also include the volatility of market return in week t (STDm,t) . The Δ operator represents the first-order difference operator. We also add lagged changes in spreads to account for any serial correlations. The interaction dummy variable DDOWN,m,t (DDOWN,i,t) takes the value of one if and only if Rm,t (Ri,t) is less than zero. This panel corresponds to Table II in the main article.
In Panel B, weekly changes in the adjusted effective spreads for each security i are regressed on signed lagged market returns with an interaction dummy variable, DCAP,t , which is equal to one when the funding market is likely to face capital constraints in week t. DCAP,t, here is set equal to one when there is a decrease in the aggregate repos on the investment bank balance sheet in week t.
titCAPtmDOWNtmkiCAPDOWNk ktmDOWNktmkiDOWNk ktmkiiti DDRDRRASPR ,1,1,,1,,,,4
1 ,,,,,4
1 ,,, variablescontrol εβββα +++∑+∑+=Δ −−−= −−= − . This panel corresponds to Table III
in the main article. In Panel C, weekly changes in the adjusted effective spreads for each security i are regressed on lagged market returns (Rm,t), idiosyncratic stock returns (Ri,t), and the change in market average spreads (ΔASPRm,t ) using the specification:
,variablescontrol ,4
1 ,,,,,4
1 ,,4
1 ,,,,,
4
1 ,,,,,,,,,,
tik ktiDOWNktikiDOWNk ktikik ktmDOWNktmkiDOWN
k ktmkitmDOWNtmiDOWNLIQtmiLIQiti
DRRDR
RDASPRbASPRbASPR
εγγβ
βα
++++
++Δ+Δ+=Δ
∑∑∑∑
= −−= −= −−
= −
where DDOWN,m,t is a dummy variable that is equal to one if and only if Rm,t is less than zero. This panel corresponds to Table V in the main article.
4
Panel A: Effective Spreads and Signed Lagged Returns
Estimated Coefficients R m,t-1 R m,t-2 R m,t-3 R m,t-4 R i,t-1 R i,t-2 R i,t-3 R i,t-4
Mean -0.298 -0.249 -0.240 -0.128 -0.361 -0.233 -0.140 -0.091 (t-statistics) (-4.03) (-3.74) (-3.68) (-2.01) (-13.14) (-9.83) (-5.93) (-3.89) Median -0.137 -0.115 -0.124 -0.055 -0.232 -0.154 -0.089 -0.054 % positive (negative) (70.3%) (69.9%) (72.6%) (61.1%) (90.9%) (89.0%) (78.7%) (71.2%) % positive (negative) significant (14.8%) (13.0%) (13.2%) (6.5%) (56.6%) (42.0%) (23.1%) (15.1%)
Estimated Coefficients R m,t-1 × DDown,m,t-1
R m,t-2 × DDown,m,t-2
R m,t-3 × DDown,m,t-3
R m,t-4 × DDown,m,t-4
R i,t-1 × DDown,i,t-1
R i,t-2 × DDown,i,t-2
R i,t-3 × DDown,i,t-3
R i,t-4 × DDown,i,t-4
Mean -0.509 -0.073 0.228 0.151 -0.069 0.016 0.009 0.043 (t-statistics) (-4.10) (-0.66) (2.08) (1.40) (-1.91) (0.37) (0.21) (1.03) Median -0.281 -0.033 0.138 0.082 -0.054 0.011 0.009 0.025 % positive (negative) (74.1%) (54.1%) 66.0% 59.7% (58.8%) 51.9% 51.8% 56.0% % positive (negative) significant (16.1%) (6.0%) 9.2% 6.6% (13.3%) 7.0% 6.3% 8.8%
Estimated Coefficients ΔSTD m,t-1 ΔSTD i,t-1 ΔTurn i,t-1 ΔOIB i,t-1 ΔSTD m, t ΔSTD i, t ΔASPR i,t-1 ΔASPR i,t-2
Mean 0.089 0.083 -0.010 0.005 0.294 0.077 -0.568 -0.381 (t-statistics) (0.92) (2.77) (-2.81) (0.67) (5.33) (4.14) (-73.72) (-44.29) Median 0.092 0.057 -0.004 0.003 0.174 0.067 -0.590 -0.395 % positive (negative) 62.0% 65.7% (67.9%) 53.3% 79.5% 70.6% (100.0%) (100.0%) % positive (negative) significant 10.7% 16.9% (13.8%) 10.0% 26.9% 32.4% (99.0%) (97.6%)
Estimated Coefficients ΔASPR i,t-3 ΔASPR i,t-4
Mean -0.241 -0.122 (t-statistics) (-28.37) (-16.32) Median -0.249 -0.122 % positive (negative) (98.2%) (95.0%) % positive (negative) significant (93.0%) (75.0%)
5
Panel B: Effective Spreads, Signed Lagged Returns, and Changes in Aggregate Repos
Estimated Coefficients R m,t-1 R m,t-2 R m,t-3~t-4 R m,t-1 ×
DDown,m,t-1 R m,t-2 ×
DDown,m,t-2 R m,t-3~t-4 ×
DDown,m,t-3~t-4 R m,t-1 × DDown,m,t-1
× DCAP,t-1
Mean -0.311 -0.256 -0.165 -0.305 -0.074 0.183 -0.493 (t-statistics) (-4.34) (-3.99) (-3.68) (-2.40) (-0.69) (2.32) (-4.93) Median -0.140 -0.124 -0.085 -0.168 -0.038 0.127 -0.284 % positive (negative) (71.2%) (72.6%) (71.4%) (64.5%) (54.0%) 69.8% (76.7%) % positive (negative) significant (14.9%) (13.4%) (12.4%) (10.0%) (6.3%) 10.5% (22.8%)
Panel C: Effective Spreads, Signed Lagged Returns, and Liquidity Betas
Estimated Coefficients R m,t-1 R m,t-2 R m,t-3~t-4 R m,t-1 ×
DDown,m,t-1 R m,t-2 ×
DDown,m,t-2 R m,t-3~t-4 ×
DDown,m,t-3~t-4 ΔASPR m,t
ΔASPR m,t × DDown,m,t
Mean -0.307 -0.185 -0.129 -0.175 -0.203 0.090 0.555 0.270 (t-statistics) (-16.82) (-11.01) (-10.84) (-5.94) (-7.53) (4.50) (40.40) (14.81) Median -0.131 -0.073 -0.059 -0.098 -0.128 0.068 0.354 0.199 %positive(negative) (70.4%) (62.2%) (66.3%) (58.7%) (63.5%) 62.0% 90.9% 71.1%
%positive(negative) significant (15.1%) (9.2%) (9.1%) (7.6%) (9.2%) 6.7% 56.8% 30.3%
6
Table IA.BII Seasonally Adjusted Quoted Spreads
The daily quoted spreads are adjusted for seasonality to obtain the adjusted spreads, ASPRi,s:
,2121 ,,5,4,3,2
,1
11
1,,
4
1,,,
sisisisisi
sik
skkik
skkisi
ASPRYEARfYEARfTICKfTICKf
HOLIDAYfMONTHeDAYdQSPR
+++++
++= ∑∑==
where we employ (i) day of the week dummies (DAYk,s) for Monday through Thursday ; (ii) month dummies (MONTHk,s) for January through November; (iii) a dummy for the trading days around holidays (HOLIDAYs); (iv) tick change dummies (TICK1s, TICK2s) to capture the tick change from 1/8 to 1/16 on 06/24/1997 and the change from 1/16 to the decimal system on 01/29/2001, respectively; (v) and time trend variables YEAR1s (YEAR2s), equal to the difference between the current calendar year and the year 1988 (1997) or the first year when the stock is traded on NYSE, whichever is later. Cross-sectional means and medians of the coefficient estimates are reported below. The mean coefficients that are significant at the 99%, 95%, and 90% confidence levels are indicated by ***, **, and *, respectively.
Estimated Coefficients Monday Tuesday Wednesday Thursday
Mean 0.005* -0.007*** -0.004** -0.003*
Median 0.000 -0.005 -0.004 -0.002
Estimated Coefficients January February March April
Mean 0.006 -0.007 -0.020 -0.019
Median 0.031 0.024 0.013 0.012
Estimated Coefficients May June July August
Mean -0.054*** -0.062*** -0.044*** -0.030**
Median -0.011 -0.017 -0.012 -0.008
Estimated Coefficients September October November Holiday
Mean -0.020* 0.028** 0.016 0.018**
Median -0.003 0.022 0.007 0.010
Estimated Coefficients Tick1 Tick2 Year1 Year2
Mean -0.579*** -0.297*** -0.047*** 0.035***
Median -0.404 -0.148 -0.040 0.000
7
Table IA.BIII Spreads and Returns: Additional Lagged Returns
Weekly changes in adjusted spreads for each security (ΔASPRi,t) are regressed on lagged market and idiosyncratic stock returns, with lagged returns of up to eight weeks: , variables control ,
8
1 ,,,,,8
1 ,,8
1 ,,,,,8
1 ,,, tik ktiDOWNktikiDOWNk ktikik ktmDOWNktmkiDOWNk ktmkiiti DRRDRRASPR εγγββα ++++++=Δ ∑∑∑∑ = −−= −= −−= −
where ASPRi,t is stock i’s seasonally adjusted proportional spread in week t; Rm,t is the week t return on the CRSP value-weighted index; and Ri,t is the idiosyncratic return on stock i in week t. The interaction dummy variable DDOWN,m,t (DDOWN,i,t) takes the value of one if and only if Rm,t (Ri,t) is less than zero. For ease of exposition, we report the coefficients for the combined market (and idiosyncratic) returns in weeks t-3 and t-4, and the combined market (and idiosyncratic) returns from week t-5 to t-8. The control variables are defined in Table II. The Δ operator represents the first-order difference of the corresponding variables. Cross-sectional means (t-statistics), medians, and percentage of significant coefficient estimates at the 5% level (one-tailed) are reported below.
Estimated Coefficients R m,t-1 R m,t-2 R m,t-3~t-4 R m,t-5~t-8 R i,t-1 R i,t-2 R i,t-3~t-4 R i,t-5~t-8
Mean -0.395 -0.344 -0.268 -0.112 -0.475 -0.316 -0.185 -0.051 (t-statistics) (-3.75) (-3.68) (-4.09) (-2.61) (-12.27) (-9.54) (-7.58) (-2.75) Median -0.214 -0.198 -0.142 -0.070 -0.333 -0.223 -0.115 -0.030 % positive (negative) (73.5%) (75.4%) (73.8%) (69.8%) (91.6%) (89.8%) (81.9%) (64.8%) % positive (negative) significant
(13.8%) (15.3%) (14.8%) (12.0%) (56.1%) (43.6%) (30.3%) (11.3%)
Estimated Coefficients R m,t-1 × DDown,m,t-1
R m,t-2 × DDown,m,t-2
R m,t-3~t-4 × DDown,m,t-3~t-4
R m,t-5~t-8× DDown,m,t-5~t-8
R i,t-1 × DDown,i,t-1
R i,t-2 × DDown,i,t-2
R i,t-3~t-4 × DDown,i,t-3~t-4
R i,t-5~t-8× DDown,i,t-5~t-8
Mean -0.833 -0.069 0.159 0.075 -0.180 0.027 0.009 -0.004 (t-statistics) (-4.67) (-0.44) (1.39) (0.89) (-2.56) (0.46) (0.20) (-0.13) Median -0.479 0.020 0.109 0.071 -0.133 0.033 0.005 0.003 % positive (negative) (77.4%) (48.8%) 62.5% 60.6% (65.1%) 54.5% 50.8% (48.7%) % positive (negative) significant
(18.8%) (4.6%) 8.3% 7.1% (16.4%) 7.2% 6.4% (5.7%)
8
Table IA.BIV Spreads and Return Dummies
Weekly changes in adjusted spreads for each security are regressed on lagged market return dummies and idiosyncratic stock return status dummies. Panel A uses the following regression specification:
,variablescontrol21 ,4
1 ,,,,4
1 ,,,,, tik ktiDOWNkiDOWNk ktmDOWNkiDOWNiti DDASPR εμμα ++++=Δ ∑∑ = −= −
where ASPRi,t is stock i’s seasonally adjusted proportional spread in week t; DDOWN,m,t (DDOWN,i,t) is a dummy variable that is equal to one if and only if Rm,t (Ri,t) is less than zero. Rm,t is the week t return on the CRSP value-weighted index; and Ri,t is the idiosyncratic return on stock i in week t. For ease of exposition, we report the coefficients for the combined market (and idiosyncratic) return dummies in weeks t-3 and t-4. The control variables are defined in Table II. The Δ operator represents the first-order difference of the corresponding variables. Panel B uses the following regression specification:
,variablescontrol21
21
,4
1 ,,,,,4
1 ,,,,,
4
1 ,,,,,4
1 ,,,,,,
tik ktiSMALLDOWNktikiSMALLDOWNk ktiLARGEDOWNktikiLARGEDOWN
k ktmSMALLDOWNktmkiSMALLDOWNk ktmLARGEDOWNktmkiLARGEDOWNiti
DRDR
DRDRASPR
εθθ
ωωα
++++
++=Δ
∑∑∑∑
= −−= −−
= −−= −−
where DDOWN LARGE,m,t (DDOWN LARGE,i,t) is a dummy variable that is equal to one if and only if Rm,t (Ri,t) is more than 1.5 standard deviations below its unconditional mean, and DDOWN SMALL,m,t (DDOWN SMALL,i,t) is a dummy variable that is equal to one if and only if Rm,t (Ri,t) is between zero and -1.5 standard deviations below its unconditional mean. Cross-sectional means (t-statistics), medians, and percentage of significant coefficient estimates at the 5% level (one-tailed) are reported below.
Panel A: Spreads and Lagged Return Dummies
Estimated Coefficients DDown,m,t-1 DDown,m,t-2 DDown,m,t-3~t-4 DDown,i,t-1 DDown,i,t-2 DDown,i,t-3~t-4
Mean 0.028 0.012 0.005 0.040 0.018 0.010 (t-statistics) (11.70) (4.89) (2.12) (16.59) (7.49) (4.33) Median 0.017 0.007 0.002 0.026 0.011 0.006 %positive(negative) 96.2% 80.0% 62.4% 97.9% 86.8% 75.7% %positive(negative) significant 62.5% 20.4% 8.1% 80.5% 34.7% 17.1%
9
Panel B: Spreads and Large/Small Lagged Return Dummies
Estimated Coefficients DDownLarge,m,t-1 DDownLarge,m,t-2 DDownLarge,m,t-3~t-4 DDownLarge,i,t-1 DDownLarge,i,t-2 DDownLarge,i,t-3~t-4
Mean 0.062 0.021 -0.003 0.088 0.032 0.018 (t-statistics) (12.59) (4.32) (-0.70) (15.11) (5.55) (3.12) Median 0.036 0.010 -0.004 0.053 0.017 0.007 %positive(negative) 95.3% 71.4% (61.0%) 95.4% 77.8% 64.9% %positive(negative) significant 63.1% 15.3% (8.6%) 71.5% 25.8% 14.5%
Estimated Coefficients DDownSmall,m,t-1 DDownSmall,m,t-2 DDownSmall,m,t-3~t-4 DDownSmall,i,t-1 DDownSmall,i,t-2 DDownSmall,i,t-3~t-4
Mean 0.022 0.010 0.007 0.036 0.017 0.009 (t-statistics) (9.15) (4.27) (2.64) (15.08) (7.03) (3.77) Median 0.014 0.006 0.003 0.023 0.010 0.005 %positive(negative) 91.9% 77.3% 66.9% 96.9% 85.7% 73.8% %positive(negative) significant 47.5% 18.6% 8.9% 74.1% 32.6% 15.5%
10
Table IA.BV Spreads and Misperceived Volatility
Weekly changes in adjusted spreads for each security are regressed on lagged market returns and idiosyncratic stock return and misperceived volatility (MisSTD) as defined in Deuskar (2007):
,variablescontrol ,1
0
1
0 ,,1
0 ,4
1 ,,4
1 ,,, tik k ktiktmk ktmk ktikik ktmkiiti STDSTDMisSTDRRASPR εγβα ++Δ+Δ+Δ+++=Δ ∑ ∑∑∑∑ = = −−= −= −= −
where ASPRi,t refers to stock i’s seasonally adjusted daily proportional quoted spread averaged across all trading days in week t; Rm,t is the week t return on the CRSP value-weighted index; Ri,t is the idiosyncratic return on stock i in week t, where idiosyncratic stock returns are calculated as individual stock returns minus market returns; STDm,t is the volatility of the market return in week t; and STDi,t is the volatility of stock i’s idiosyncratic returns in week t. Other control variables are defined in equation (2) in the text. The Δ operator represents the first-order difference of the corresponding variables.
Estimate Statistics R m,t-1 R m,t-2 R m,t-3 R m,t-4 R i,t-1 R i,t-2 R i,t-3 R i,t-4
Mean -0.990 -0.505 -0.236 -0.151 -0.584 -0.312 -0.191 -0.099 (t-statistics) (-18.12) (-10.19) (-4.83) (-3.11) (-29.79) (-15.82) (-9.68) (-5.05) Median -0.704 -0.343 -0.130 -0.073 -0.464 -0.233 -0.137 -0.059 % positive (negative) (96.0%) (86.6%) (67.4%) (61.9%) (98.2%) (93.0%) (82.7%) (69.7%) % positive (negative) significant
(66.4%) (37.1%) (13.1%) (10.0%) (86.4%) (56.5%) (32.8%) (14.3%)
Estimate Statistics ΔSTD m,t-1 ΔSTD i,t-1 ΔSTD m, t ΔSTD i, t ΔMisSTD i,t-1 ΔMisSTD i,t ΔTurn i,t-1 ΔOIB i,t-1
Mean 0.311 0.274 0.280 0.241 0.940 0.455 -0.024 0.007 (t-statistics) (2.21) (3.55) (7.06) (10.00) (5.51) (11.00) (-4.04) (0.71) Median 0.263 0.168 0.204 0.193 0.619 0.334 -0.013 0.006 % positive (negative) 64.3% 66.9% 78.7% 84.7% 75.4% 87.2% (75.4%) 54.0% % positive (negative) significant
12.9% 13.8% 25.2% 40.7% 36.9% 45.8% (19.4%) 8.1%
11
Table IA.BVI Proportion of Small Trades and Market Returns
Weekly changes in percentage of small trades for each security (ΔSmallTrade%i,t) are regressed on lagged market and idiosyncratic stock returns:
, variablescontrol
%
,4
1 ,,,,,,,4
1 ,,,
4
1 ,,,,,4
1 ,,,,,,
tik ktiDOWNktikiDOWNktiUPk ktikiUP
k ktmDOWNktmkiDOWNk ktmUPktmkiUPiti
DRDR
DRDRSmallTrade
εγγ
ββα
++++
++=Δ
∑∑∑∑
= −−−= −
= −−= −−
where SmallTrade%i,t is the number of small trades, defined as the trade whose size is below $5000, divided by the total number of trades for stock i in week t; Rm,t is the week t return on the CRSP value-weighted index; and Ri,t is the idiosyncratic return on stock i in week t. The interaction dummy variable DUP,m,t (DUP,i,t) takes the value of one if and only if Rm,t (Ri,t) is greater than zero, and the interaction dummy variable DDOWN,m,t (DDOWN,i,t) takes the value of one if and only if Rm,t (Ri,t) is less than zero. The control variables are defined in Table II. The Δ operator represents the first-order difference of the corresponding variables. Cross-sectional means (t-statistics), medians, and percentage of significant coefficient estimates at the 5% level (one-tailed) are reported below.
Estimated Coefficients R m,t-1 × DUp,m,t-1
R m,t-2 × DUp,m,t-2
R m,t-3 × DUp,m,t-3
R m,t-4 × DUp,m,t-4
Mean 0.073 0.044 0.042 0.041 (t-statistics) (3.45) (2.32) (2.25) (2.25) Median 0.042 0.026 0.026 0.008 % positive (negative) 56.3% 54.4% 54.9% 52.2% % positive (negative) significant 9.2% 6.7% 6.4% 5.2%
Estimated Coefficients R m,t-1 × DDown,m,t-1
R m,t-2 × DDown,m,t-2
R m,t-3 × DDown,m,t-3
R m,t-4 × DDown,m,t-4
Mean 0.011 0.013 0.008 0.019 (t-statistics) (0.58) (0.69) (0.43) (1.02) Median 0.001 0.000 0.000 0.000 % positive (negative) 50.1% 49.4% 47.7% 47.3% % positive (negative) significant 5.3% 5.0% 4.5% 4.2%
12
Table IA.BVII Spreads, Market Returns, and Impact of the Funding Market Proxies
Weekly changes in the adjusted spreads for each security (ΔASPRi,t) are regressed on signed lagged market returns with an interaction dummy variable DCAP,t that is equal to one when the funding market is likely to face capital constraints in week t:
tik ktCAPktmDOWNktmkiCAPDOWNk ktmDOWNktmkiDOWNk ktmkiiti DDRDRRASPR ,4
1 ,,,,,,,4
1 ,,,,,4
1 ,,, variablescontrol εβββα +++++=Δ ∑∑∑ = −−−= −−= −.
All other variables are defined in Table II. In Panel A, DCAP,t is equal to one when the excess return on a portfolio of investment banks in week t is negative. DCAP,t in Panel B is equal to one when there is a decrease in the aggregate repos in week t. Finally, when there is an increase in the commercial paper spread, we assign a value of one to DCAP,t in Panel C. For ease of exposition, we report the coefficients for the combined market (and idiosyncratic) returns and funding market constraint dummies in weeks t-3 and t-4. Cross-sectional means (t-statistics), medians, and percentage of significant coefficient estimates at the 5% level (one-tailed) are reported below.
Panel A: Investment Bank & Broker Sector Returns
Estimated Coefficients R m,t-1 R m,t-2 R m,t-3~t-4 R m,t-1 ×
DDown,m,t-1 R m,t-2 ×
DDown,m,t-2 R m,t-3~t-4 ×
DDown,m,t-3~t-4
Rm,t-1 × DDown,m,t-1 ×
DCAP,t-1
Rm,t-2 × DDown,m,t-2 ×
DCAP,t-2
Rm, t-3~t-4 × DDown,m,t-3~t-4 ×
DCAP,t-3~t-4
Mean -0.422 -0.326 -0.226 -0.658 -0.052 0.154 -0.302 0.009 0.087 (t-statistics) (-4.23) (-3.67) (-3.66) (-3.75) (-0.33) (1.26) (-2.26) (0.07) (0.83)
Median -0.215 -0.193 -0.118 -0.354 0.030 0.119 -0.153 -0.002 0.015 % positive (negative) (73.8%) (73.6%) (70.5%) (72.0%) (47.9%) 62.6% (61.5%) 49.7% 51.9% % positive (negative) significant (15.0%) (15.4%) (11.8%) (14.9%) (4.6%) 8.6% (10.6%) 4.6% 7.1%
13
Panel B: Change in Repos
Estimated Coefficients R m,t-1 R m,t-2 R m,t-3~t-4 R m,t-1 ×
DDown,m,t-1 R m,t-2 ×
DDown,m,t-2 R m,t-3~t-4 ×
DDown,m,t-3~t-4
Rm,t-1 × DDown,m,t-1 ×
DCAP,t-1
Rm,t-2 × DDown,m,t-2 ×
DCAP,t-2
Rm, t-3~t-4 × DDown,m,t-3~t-4 ×
DCAP,t-3~t-4
Mean -0.450 -0.334 -0.214 -0.490 -0.176 0.156 -0.655 0.307 0.138 (t-statistics) (-4.61) (-3.84) (-3.54) (-2.84) (-1.14) (1.35) (-4.83) (2.26) (1.32)
Median -0.249 -0.196 -0.114 -0.242 -0.044 0.111 -0.367 0.191 0.070
% positive (negative) (76.0%) (74.2%) (69.3%) (66.6%) (53.5%) 62.3% (74.9%) 66.2% 58.5% % positive (negative) significant (16.3%) (15.9%) (11.0%) (9.7%) (6.2%) 6.8% (20.2%) 11.0% 6.8%
Panel C: Commercial Paper Spread
Estimated Coefficients R m,t-1 R m,t-2 R m,t-3~t-4 R m,t-1 ×
DDown,m,t-1 R m,t-2 ×
DDown,m,t-2 R m,t-3~t-4 ×
DDown,m,t-3~t-4
Rm,t-1 × DDown,m,t-1 ×
DCAP,t-1
Rm,t-2 × DDown,m,t-2 ×
DCAP,t-2
Rm, t-3~t-4 × DDown,m,t-3~t-4 ×
DCAP,t-3~t-4
Mean -0.434 -0.323 -0.219 -0.500 -0.147 0.242 -0.458 0.137 -0.062 (t-statistics) (-4.35) (-3.61) (-3.56) (-2.62) (-0.84) (1.85) (-3.40) (1.01) (-0.57)
Median -0.239 -0.187 -0.113 -0.254 -0.032 0.137 -0.263 0.073 0.004
% positive (negative) (74.7%) (73.4%) (70.0%) (65.3%) (52.4%) 62.2% (71.7%) 57.0% (49.2%) % positive (negative) significant (15.7%) (14.5%) (11.3%) (8.5%) (6.0%) 7.7% (14.1%) 6.6% (5.1%)
14
Table IA.BVIII Contrarian Profits, Market Returns, and Liquidity Commonality
Weekly stock returns are sorted into winner (loser) portfolios if the returns are above (below) the median of all positive (negative) returns in week t. The contrarian portfolio weight for stock i in week t is given by
∑ = −−−−=Np
i tititititip TurnRTurnRw1 1,1,1,1,,, /)( , where Ri,t and Turni,t are stock i’s return and turnover in week
t. We report contrarian profits conditional on market returns and liquidity commonality. Large Up (Large Down) refers to cumulative market returns from week t-4 to t-1 being more than 1.5 standard deviations above (below) the mean. Small Up (Small Down) market refers to cumulative market returns between zero and 1.5 (-1.5) standard deviations. We further split the sample based on whether liquidity commonality is above (below) the median.
Week t+1 Past Market Return:
Large Up Small Up Small Down Large Down Liquidity
Commonality: Liquidity
Commonality: Liquidity
Commonality: Liquidity
Commonality: Portfolio
High Low High Low High Low High Low
loser 1.40% -0.33% 0.97% 0.69% 0.39% 0.56% 1.99% 0.74% winner 0.67% -0.87% 0.52% 0.06% -0.06% -0.02% 0.27% 0.11% loser-winner 0.73% 0.55% 0.44% 0.63% 0.45% 0.58% 1.73% 0.64% (t-statistic) (0.98) (0.56) (2.09) (3.71) (1.21) (3.04) (3.16) (1.40) Week t+2
Past Market Return: Large Up Small Up Small Down Large Down Liquidity
Commonality: Liquidity
Commonality: Liquidity
Commonality: Liquidity
Commonality: Portfolio
High Low High Low High Low High Low
loser 1.07% 0.65% 0.55% 0.33% 0.13% 0.28% 1.76% 0.17%
winner 0.87% -0.01% 0.53% 0.28% -0.10% 0.27% 0.45% -0.32%
loser-winner 0.19% 0.66% 0.02% 0.05% 0.23% 0.01% 1.31% 0.49%
(t-statistic) (0.41) (1.28) (0.13) (0.35) (1.08) (0.06) (1.91) (0.70)
15
REFERENCES
Engle, Robert, 2002, Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models, Journal of Business & Economic Statistics 20, 339-350.
Dueskar, Prachi, 2007, Extrapolative expectations: Implications for volatility and liquidity, Working paper, University of Illinois at Urbana-Champaign